New Century Maths 10 - Wikispaces · 88 NEW CENTURY MATHS 10: STAGES 5.1/5.2 e During the early 1990s the unemployment rate was 10% in Australia. (Compare …

84

N EW CENTURY MATHS 10 : S TAGES 5 .1/5 .2

1 Simplify each of the following, leaving your answer as a fraction:

a b c d e

f g h i j

2 Out of every 100 people at a football game, 61 were men, 29 were women and the rest were children. Find the following ratios.a men : women b women : the totalc children : men d women : children

3 In a classroom of 27 students, 13 students had brown hair, 8 had black hair, 5 had blonde hair and the remainder had red hair. Find the ratio of students with the following hair colours.a red to blonde b brown to black c red to brown d blonde to brown

4 For each of the following diagrams, find:i the ratio of shaded area to unshaded area

ii the ratio of shaded area to the total area.

a b c

5 Express each of these statements as a ratio.a Ruby and Loretta agree to share the work equally.b Ben has twice as many merit certificates as Khodr.c Sue is half the height of Ketsana.d There must be one teacher for each 30 students on the excursion.e There are 13 girls for every 12 boys in this school.f The expressway cost five times the amount budgeted.g The puppy is one-tenth the weight of the adult dog.h You need 1 cup of rice to 2 cups of boiling water to cook rice.i The Sun is a million times hotter than a lighted match.j The train journey took one-and-a-half times as long as the road journey.

510------ 10

5------ 6

8--- 8

6--- 9

12------

129------ 20

25------ 25

20------ 70

100--------- 100

70---------

Start up

Worksheet 3-01

Brainstarters 3

Skillsheet 1-03

Simplifying fractions

Simplifying fractions and ratiosWhen simplifying a fraction or a ratio, look for a common factor to divide into both the numerator and the denominator. The higher the factor, the better. Remember the divisibility tests as shown in this table.

A number isdivisible by:

if:

2 it is even (its last digit is 2, 4, 6, 8 or 0)

3 the sum of its digits is divisible by 3

4 its last two digits form a number divisible by 4

5 its last digit is 0 or 5

6 it is even and the sum of its digits is divisible by 3

9 the sum of its digits is divisible by 9

10 its last digit is 0

Skillbank 3

SkillTest 3-01

Simplifying fractions and

ratios

03_NCMaths_10_2ed_SB_TXT.fm Page 84 Thursday, April 14, 2005 1:45 PM

R A T IOS AND RA TES

85

CHAPTER 3

1 Examine these examples.

a Simplify

= = (dividing numerator and denominator by 3)

= (dividing numerator and denominator by 3 again)

Note: This fraction could be simplified more quickly (in one step) if you just divided by 9, the highest common factor (HCF).

b Simplify

= = (dividing numerator and denominator by 10)

= (dividing numerator and denominator by 4)


Note: This fraction could be simplified more quickly if you just divided by 80, the HCF.

c Simplify the ratio 24 : 36.

24 : 36 = = 4 : 6 (dividing both numbers by 6)

= 2 : 3 (dividing both numbers by 2)d Simplify the ratio 135 : 90.

135 : 90 = = 27 : 18 (dividing both numbers by 5)

= 3 : 2 (dividing both numbers by 9)

e Calculate in simplest form.

= (dividing 2 and 8 by 2)


=

f Calculate in simplest form.



=

g What fraction is 36 minutes of 1 hour?

=



=

2745------.

2745------ 27

45------

9

15

915------

915------

3

5

35---

160400---------.

160400--------- 160

400--------- 16

40------

1640------

4

10

410------

410------

2

5

25---

244 : 366

42 : 63

13527 : 9018

273 : 182

38--- 2

15------×

38--- 2

15------× 3

8--- 2

15------×

4

1

38--- 2

15------×

4

11

51

20------

5 8×12 35×------------------

5 8×12 35×------------------ 5 8×

12 35×------------------1

7

5 8×12 35×------------------1

73

2

221------

36 min1 h

---------------- 36 min60 min----------------

3660------

6

10

610------

3

535---

and

and


86

N EW CENTURY MATHS 10 : S TAGES 5 .1/5 .2

Ratios

Simplifying ratios

2 Now simplify these:

a b c d

e f g h

i 20 : 36 j 25 : 45 k 18 : 40 l 28 : 35

m 27 : 21 n 16 : 12 o p

q r s t

3 Express these as simplified fractions.a 425 g of 1 kg b 8 months of 1 year c 64 cm of 1 md 750 mL of 3 L e 10 hours of 2 days f 80c of $10

1015------ 16

20------ 30

42------ 8

16------

2080------ 6

36------ 20

24------ 12

30------

56--- 18

25------× 12

50------ 10

21------×

1516------ 8

30------× 7 40×

10 63×------------------ 20 9×

32 36×------------------ 6 5×

30 4×---------------

A ratio is a relationship that compares quantities of the same type that are (or can be) measured in the same units.

Skillsheet 3-01Ratios

Example 1

Express the ratio of 350 mL to 2.5 L in simplest form.

SolutionWhen simplifying a ratio, the units of each part of the ratio need to be the same.

350 mL : 2.5 L = 350 mL : 2500 mL (changing both quantities to the same unit)

= 350 : 2500

= 7 : 50

Simplify the ratio 24 : 18 : 48.

Solution24 : 18 : 48 = 4 : 3 : 8 (dividing each term by 6)

Note: The calculator cannot be used with ratios of three or more terms.

Example 2

1 Simplify each of the following ratios:a 55 : 66 b 14 : 12 c 81 : 118 d 35 : 42e 5 : 105 f 1200 : 900 g 46 : 253 h 90 : 25i 48 : 36 j 96 : 144 k 36 : 25 l 24 : 42m 34 : 136 n 275 : 175 o 45 : 20 p 84 : 56

Exercise 3-01Spreadsheet 3-01

Simplifying ratios

SkillBuilder5-01

Introduction to ratio


RAT IOS AND RA TES 87 CHAPTER 3

2 Simplify each of these ratios:

a b c d

e f g h

i 10 : j 4 : k : 2 l : 3

3 Simplify each of the following ratios:a 0.7 : 0.5 b 1.3 : 0.8 c 3.6 : 2.4 d 2.5 : 0.05e 3.02 : 0.16 f 4.4 : 22 g 0.05 : 0.005 h 5.6 : 1.28i 5 : 2.25 j 1.08 : 8.1 k 1.25 : 0.0625 l 13.2 : 0.64

4 Express each of these as a ratio in its simplest form:a 10 litres to 25 litres b $30 to $3 c 1500 m to 100 md 200 km to 40 km e 44 kg to 66 kg f 625c to 875c

5 For each of the following ratios, change the quantities to the same units and then simplify:a 50c to $1 b 40 min to 1 hour c 75 mL to 1 Ld 30 min : 5 hours e 4 days : 4 weeks f 300 mm : 3 mg 5 mm to 4 cm h $4 : 50c i 5 min to 20 sj $3.75 : 25c k 5 km to 30 m l 750 mL : 2 Lm 20 g : 1 t n 1 hour 30 min : 40 min o 80 g : 24 kg

6 Simplify each of the following ratios:a 15 : 10 : 35 b 120 : 20 : 80 c 49 : 84 : 28

d 27 : 36 : 18 e 4 : : 3 f : 1

g h 0.8 : 1.4 : 1.0 i 14.4 : 8.4 : 12.0

7 Simplify each of the following ratios:a $5 : $20 : $100 b 15 min : 2 h : 1 h c 96 cm : 1.44 mm : 12 cmd 4 kg : 400 g : 40 g e 2 L : 1 L : 375 mL f $90 : $3 : 75c

8 A square has sides of 10 cm. Find the ratio of the side length to the perimeter.

9 A rectangle has a length of 8 cm and a breadth of 5 cm. Find the ratio of the length to the perimeter.

10 Find the ratio of an angle of 45° to:a its complement b its supplement.

11 Find the ratio of an angle of 60° to:a a right angle b a straight angle c an angle of revolution.

12 Express each of these statements as a ratio in its simplest form.a My grandparents’ clock loses 5 minutes every hour. (Compare the minutes lost to the hours

passed.)b In a race, first place increases the lead over second place by 10 metres every kilometre that

is run. (Compare the increase in the lead to the kilometres run.)c A fast-food company agrees to donate 5c out of every $1 purchased to charity. (Compare

the donation to the dollars spent on purchases.)d Bob and Sue are filling 1 litre containers. On average they spill 25 mL with each filling.

(Compare the amount spilled to the litres filled.)

34--- : 2

3--- 1

5--- : 5

6--- 2

3--- : 1

4--- 7

8--- : 2

3---

35--- : 2

3--- 11

2--- : 3

4--- 22

3--- : 4

5--- 11

4--- : 22

3---

35--- 2

3--- 1

2--- 21

2---

12--- 3

4--- : 2

3--- : 1

34--- : 1

5--- : 1

2---

Example 1

Example 2

Spreadsheet 3-02

Simplifying fraction ratios


88 NEW CENTURY MATHS 10 : S TAGES 5 .1/5 .2

e During the early 1990s the unemployment rate was 10% in Australia. (Compare the number of unemployed to the total workforce.)

f A store gives a 15% discount to its permanent employees. (Compare the discounted price to the marked price.)

g A new baby needs 50 g of food for each kilogram of body mass. (Compare the food needed to body weight.)

h A cheap watch gains 10 seconds every minute. (Compare the seconds gained to the minutes passed.)

i A marathon runner has as little as of total body mass made up of

body fat. (Compare body fat to total body mass.)

j A new car loses of its value in the first year. (Compare the loss in value to the original value.)

120------

1212---%

The golden ratioSome rectangles appear more pleasing to look at than others. Such rectangles are close approximations to a special rectangle known as the golden rectangle. Two of the three rectangles in the diagram on the right are golden rectangles.

In architecture, many window designs are based on golden rectangles, as are buildings such as the Parthenon in Athens (shown in the photo).

Just for the record



Applying ratiosRatio problems can be solved using equivalent ratios or the unitary method. The unitary method requires finding one part first.

The relationship between the two sides of a golden rectangle can be expressed as follows:

The ratio of the long side to the short side is equal to the ratio of the sum of the two sides to the long side.

This ratio, known as the golden ratio is = 1.618 034 …

The ratio can be expressed as =

The golden ratio is applied when appearances are important.

1 Investigate the length to width ratio of envelopes, stamps, flags, postcards, playing cards and paintings. How close to the golden ratio is their ratio of length to width?

2 Research one of the following:• the golden ratio • divine proportion• golden section • the Parthenon

1 5+2

----------------

lengthwidth--------------- length width+

length-----------------------------------.


Example 3

At a school canteen the ratio of salad rolls to pies sold is 4 : 5. If 250 pies were sold, how many salad rolls were sold?

SolutionLet x be the number of salad rolls.Method 1: Method 2:

4 : 5 = x : 2504 : 5 = x : 250

Since 5 × 50 = 250=

x = 4 × 50

= x = 200

= 200∴ 200 salad rolls were sold.

A new car dealer finds that the ratio of sedans to station wagons sold is 20 : 7. If 600 sedans were sold, how many station wagons were sold?

Solutionsedans : station wagons = 20 : 7Since 600 sedans were sold:20 parts = 600∴ 1 part = 600 ÷ 20

= 307 parts = 30 × 7

= 210∴ 210 station wagons were sold.

x250--------- 4

5---

x250--------- 250×

1

1 45--- 250×1

50

Example 4



1 During a summer sale the ratio of jeans to shorts sold was 2 : 9. If 240 jeans were sold, how many shorts were sold?

2 The ratio of the age of a father to the age of his daughter is 8 : 3. If the daughter’s age is 12, find:a the age of the father b the ratio of their ages after another 6 years.

3 Two people invest in a business in the ratio 5 : 7. If the larger investment is $63 000, find the smaller investment.

4 Patricia and Hula have a garage sale and agree to share the profits in the ratio 3 : 4. If Hula receives $195.60, how much will Patricia get?

5 A quick recipe for paste requires adding 2 cups of cornflour to every 3 cups of boiling water, then stirring vigorously to dissolve before allowing it to cool.a For 12 cups of water, how much flour is needed?b If 6 cups of flour are used, how much water is needed?c For 15 cups of water, how much flour is needed?d If 8 cups of flour are used, how much water is needed?

6 A survey of car buyers found that they purchased cars with colours in the ratio of white : red : other colour = 12 : 8 : 5.a What fraction of the total cars surveyed was white? Express this as a percentage.b If a dealer ordered 25 cars in colours other than red or white, how many red cars and white

cars should be ordered?

7 In one year, a recycling depot found that it recycled 43 kg of paper for every 1 kg of plastic bottles and 6 kg of glass recycled.a What is the ratio of paper : plastic : glass?b What percentage of waste recycled is plastic?c If, on average, the depot recycled 1.935 tonnes of paper a week, calculate the weekly

quantities of glass and plastic recycled.d After an advertising campaign the weekly quantities of paper : plastic : glass recycled

changed to 48 : 5 : 7. What percentage of the waste now recycled is plastic?

8 The axle ratio of a motor vehicle is the number of revolutions of the drive shaft made for every turn of the rear wheels. An axle ratio of 8 : 1 means that the drive shaft makes eight revolutions for every turn of the rear wheel.a A car has an axle ratio of 10 : 1. How

many times will the drive shaft rotate for 100 turns of the rear wheel?

b If the drive shaft turns 2000 times, how many times will the rear wheel turn if the axle ratio is:i 4.5 : 1? ii 8 : 3?

9 A school sells tracksuits in school colours. The ratio of size 12 : size 14 : size 16 : size 18 sold is 3 : 5 : 6 : 8. Suppose that the school sold 240 size 14 tracksuits.a How many tracksuits did the school sell in other sizes?b How many tracksuits did it sell altogether?

Engine

Drive shaft

Exercise 3-02

Example 4

Example 3

Spreadsheet 3-03

Equivalent ratios

Spreadsheet 3-04

Ratios and the unitary method



Dividing a quantity in a given ratio

IcebergsAn iceberg is a large mass of ice which has become detached from a glacier and then floats out to sea. Most of an iceberg is submerged.

The ratio of the volume of an iceberg above the water to the volume of the iceberg below the water is about 1 : 7.

In 2003, the world’s largest iceberg, named B15, split into two pieces during a storm. Located off the Ross ice shelf in Antarctica, the iceberg had an area of 11 000 km2, the same size as the country of Jamaica! The largest iceberg is now C19A, with an area of 5659 km2. It is situated near a French Antarctic base.

If the mass of the part of an iceberg above water is 2000 t, what is the total mass of the iceberg?

Just for the record

Example 5

Tracy and Curtis share $195 in the ratio 11 : 4. How much will each of them receive?

SolutionThe given ratio has a total of 15 parts (11 + 4) = 15.Method 1: Unitary method∴ 15 parts = $195

1 part = $195 ÷ 15= $13

∴ Tracy’s share = 11 × $13= $143

Curtis’s share = 4 × $13= $52

Method 2: Fraction method

Tracy’s share = of $195

= $143

Curtis’s share = of $195

= $52

1115------

415------


Worksheet3-02Ratio

calculations

Worksheet3-03

Ratio problems

1 Divide each of the following in the ratio given.a $30 [2 : 3] b 125 L [3 : 7]c 60 marbles [7 : 5] d 3000 m [9 : 6]e 224 g [3 : 4] f 16 t [7 : 9]g $76 [5 : 3] h $5000 [2 : 3 : 5]i 30 kg [1 : 6 : 1] j 315 cm [4 : 2 : 3]

2 A survey at an intersection showed that the ratio of cars running the red light to cars stopping was 27 : 1973. If 72 000 cars passed through the intersection last week, how many red-light camera tickets would you expect to be issued?

Exercise 3-03Example 5

Spreadsheet 3-05

Dividing quantities in a

given ratio

SkillBuilders

5-02 to 5-03Dividing a given

ratio



3 Of every 30 telephone calls that Colin makes, 7 are STD calls. If he made 360 calls, how many of them were STD calls?

4 Out of a class of 30 students, five speak more than one language. Estimate how many of the school’s 450 students speak more than one language.

5 Copy the number line below into your workbook. Show the points that divide the interval AB in the ratio:a 1 : 1 b 1 : 2 c 3 : 1 d 7 : 2

6 An alloy consists of nickel and copper in the ratio of 4 : 7. If the alloy weighs 3.41 kg, how much of each metal was used?

7 The masses of three students are in the ratio 4 : 5 : 8. If their combined mass is 204 kg, find the mass of the heaviest student.

8 Randa and Dwayne share a part-time job doing the local milk run. Randa works three afternoons and Dwayne works two afternoons. If they earn $215 per week altogether, how much do they each earn?

9 Twenty-four-year-old Ruby and 26-year-old Ben agree to share a lottery win of $20 000 in the ratio of their ages. How much does each receive?

10 Two couples begin a business. Bob and Sue invest $40 000, while Ted and Anita invest $30 000. In the first year, the business makes a profit of $210 000. Divide the profit in the ratio of their investments.

11 One paddock measures 15 m2 and another measures 35 m2. Divide a kilogram packet of grass seed between the two paddocks in the ratio of their areas.

12 A concrete mixture of gravel to sand to cement of 4 : 3 : 1 is needed for strong foundations. How much of each ingredient is needed to make 60 cubic metres of concrete?

13 Gold jewellery is classified according to its gold content. The ratio of the amount of gold to the amount of other metals is given in carats. Pure gold is 24 carat and 10 carat gold is gold mixed with other metals in the ratio 10 : 14.a Write a ratio to describe the gold in:

i a 12 carat chainii an 18 carat ring

b Chris purchases a 9 carat medallion with a mass of 48 g. How much gold is in the medallion?

14 A will stipulates that, for each 40 cents Thomas receives, Svetlana will receive 30 cents and Amadullah will receive 55 cents. How much will they each receive from an inheritance of $1 million?

15 Share a box of 364 lollies between three children so that, for every 50 lollies Patricia receives, Jessop receives 30 lollies and Nubia receives 25 lollies.

16 The sizes of four angles at a point of revolution are in the ratio 4 : 2 : 1 : 3. Calculate the size of each angle.

17 The lengths of the sides of a triangle are in the ratio 5 : 3 : 7. If the perimeter of the triangle is 31.5 cm, find the length of the shortest side.

−6

A B

−4 −2−5 −3 −1 0 2 4 61 3 5



Scale drawingsA scale drawing is a diagram that accurately represents a larger or smaller real object. This means that the scale drawing is either a reduction or an enlargement of the real object. The scale factor used is referred to as the scale of the drawing.

Scales may be represented in the following ways:• 1 cm = 10 km (a pair of corresponding measurements)• 25 : 1 (a ratio in the form a : 1)• 1 : 1000 (a ratio in the form 1 : b)

• (a line drawn to scale)

• (a line and a ratio)

A scale written in the form a : 1 (such as 600 : 1) represents an enlargement of a real object.

A scale written in the form 1 : b (such as 1 : 5000) represents a reduction of a real object.

Worksheet3-04

Interpreting an office plan

Worksheet3-05

Scale drawings

Worksheet3-06

Problems involving

scale drawings

kilometres kilometres0 1 2 3 4 5

1 : 40 000 000 0 500 1000 1500

Example 6

Express the following scales in the form a : 1 or 1 : b.a 2 cm to 5 m b 15 m : 10 cm

Solutiona 2 cm to 5 m = 2 cm : 5 m

= 2 cm : 500 cm (same units)

= (dividing by the smaller number)

= 1 : 250b 15 m : 10 cm = 1500 cm : 10 cm (same units)

= (dividing by the smaller number)

= 150 : 1

1 The scale drawing on the right is an accurate diagram of a block of land in a Sydney suburb.What is the actual length of the boundary XY?

SolutionThe length of XY = 50 mm and the scale is 1 : 1000.∴ Actual length of XY = 1000 × 50 mm

= 50 000 mm= 50 m (since 1 m = 1000 mm)

2 The scale on a map is 1 : 50 000. What distance is represented by a length of 60 mm on the map?

SolutionLength on the map = 60 mm∴ Actual distance = 50 000 × 60 mm

= 3 000 000 mm= 3000 m= 3 km

22--- : 500

2---------

150010

------------ : 1010------

Scale 1 : 1000

Lot 15Area = 1093 m2

Y

X

Example 7



Example 8

A computer chip is drawn to a scale of 40 : 1. Find the actual length of the chip if the measured length on the scale drawing is 80 mm.

SolutionSince the scale is 40 : 1 (scale factor = 40), the scale drawing is an enlargement.∴ Actual length = 80 mm ÷ 40

= 2 mm

1 Change each of the following scales to a ratio in the form 1 : a, or b : 1a 1 cm to 5 m b 1 mm : 10 cm c 10 m : 0.5 cmd 2 cm : 1 km e 10 cm to 1 m f 2 mm to 1 cmg 5 m : 2 cm h 10 m : 1 cm i 5 cm to 10 kmj 4 m to 5 mm k 15 mm : 12 cm l 5 cm to 6 kmm 20 m to 4 cm n 8 cm to 75 m o 2 mm to 25 m

2 The following lines have been drawn using a scale of 1 : 50. What distance (in metres) does each represent?a b cd e

3 A scale of 1 : 200 is used to draw a line representing a distance of 5 m. Which of the following is the length of the line?A 25 m B 25 cm C 25 mm D 2.5 mm

4 The scale on a map is 1 : 25 000. What distance is represented by a length of 33 mm on the map?

5 This scale drawing of a holiday house is to a scale of 1 : 200. What is the actual length of:a distance PN?b distance MN?

6 The following lines have been drawn using a scale of 20 : 1. What distance (in millimetres) does each represent?a bc d e

7 A scale of 10 : 1 is used to draw a line which is to represent an actual distance of 5 mm. Which of the following will the length of the line be?A 5 cm B 50 cm C 5 m D 0.5 cm

8 A scale of 1 : 100 is the same as which of the following scales?A 1 cm : 1 km B 5 cm : 1 km C 1 mm : 1 m D 2 mm : 20 cm

P

T W

Q M

N

Exercise 3-04

Example 7

Example 6

Example 8

Spreadsheet 3-06

Converting scales to ratios



9 A scale of 1 : 1000 is the same as which of the following scales?A 1 cm : 1 m B 1 mm : 1 m C 5 mm : 1 m D 1 cm : 100 m

10 On a map, a distance of 30 km is shown by 1.5 cm. What scale has been used?

11 Express the scale 1 cm to 250 km as a ratio in the form 1 : a.

12 This map shows Moreton Island, which is off the Australian coast just north of Brisbane.a Use the scale to find the distance

from:i Cape Moreton to Tangalooma

ii Tangalooma to Deception Bay.b What is the maximum width of

Moreton Island (in kilometres)?c What is the maximum length of

Moreton Island (in kilometres)?d Use the scale to estimate the width

of Mud Island.

13 The map below shows part of the coast of New South Wales.

a Use the scale to find the distance from:i Laurieton to Wollongong

ii Newcastle to Kandosiii Campbelltown to Moss Vale

b Which town is 130 km from Lithgow?

Caboolture

Petrie

StrathpineSandgate

Mud Island

Redcliffe

DeceptionBay

Bongaree

Tangalooma

Cape Moreton

0 10Scale

km

20

MoretonIsland

Laurieton

Taree

Forster

Maitland

NewcastleCessnock

Singleton

Muswellbrook

Mudgee

Kandos

Lithgow

KatoombaPenrith Sydney

Campbelltown

Wollongong Scale

km

Camden

Mittagong

Goulburn

Moss Vale Nowra

Gosford

0 40 80 120 160 200



RatesA rate measures how one quantity changes with respect to another quantity.

Some examples of rates are:• speed, which compares distance travelled with time. A speed of 120 km/h means 120 km are

travelled each hour.• heartbeat rate, which compares number of heartbeats with time. A heartbeat rate of 100 beats

per minute means 100 heartbeats every minute.• fuel consumption rate, which compares distance travelled with volume of fuel used. A fuel

consumption rate of 8 km/L means the car will travel 8 km for every litre of petrol. However, fuel consumption is more commonly measured in L/100 km. For example, 12.5 L/100 km means 12.5 litres of fuel are used for every 100 km travelled.

Simplifying ratesA rate is usually expressed in the form of a quantity per unit. For example, a speed of 255 kilometres in 3 hours is better expressed in the simplified form of 85 kilometres per one hour.

14 a Express the scale 25 mm to 500 km as a ratio in the form 1 : a.b The scale 25 mm to 500 km is used to draw a map of Australia. If the maximum width of

Australia on the map is approximately 20 cm, calculate the actual width of Australia.

15 On the right, a rectangular room has been drawn to scale. The length of the room is 4.5 m.a Determine the scale that has been used.b What is the width of the door?

4500

3800

Worksheet 3-07

Rates problems

A rate compares quantities of different types that are measured in different units.

Worksheet 3-08

Speed problems

Example 9

Write each of the following as a rate:a assembling 48 mountain bikes in an 8-hour shiftb $183 for 20 international telephone calls

Solutiona 48 mountain bikes in 8 hours = 48 ÷ 8

= 6 bikes/hourb $183 for 20 international calls = $183 ÷ 20

= $19.15/call



Applying rates

Note: Rate problems are solved by either multiplying or dividing.

Once simple rule for deciding whether to multiply or to divide is to examine the position of the required quantity in the rate, written in the form x/y.• To find the first quantity, x, you multiply.• To find the second quantity, y, you divide.

Example 15 used the rate km/h.• To find the number of kilometres (in part b), you multiply.• To find the time, in hours, you would divide.

The beat goes onThe heart of an unfit person works harder whether at rest, during activity and even while recovering from activity. A fit person’s heart copes with activity better and its beat returns to normal sooner.

What patterns do you notice in the differences in heartbeat rates between fit and unfit persons?

Heartbeats per minute

Fit Unfit Difference

Before activity 65 80 15

During activity 95 135 40

3 minutes after 80 115 35

6 minutes 70 100 30

9 minutes after 65 95 30

Just for the record

Example 10

A car travels 235 km in 5 hours.a Calculate its average speed (in km/h). b How far does the car travel in hours?

Solutiona Speed = 235 km in 5 hours b Distance in hours = 47 ×

= km/h = 352.5 km

= 47 km/h

712---

712--- 71

2---

2355

---------



1 Write each of the following as a rate:a 450 km in 5 h [km/h] b $108 in 3 h [$/h]c 12 L for 156 km [km/L] d 8 kg for $6.40 [c/kg]e 144 mm in 8 h [mm/h] f 25 telephone calls for $19 [cents/call]g $54.40 for 1.6 metres [$/m] h 10 000 parts in 8 hours [parts/h]i 12 bottles for $99 [$/bottle] j 36 days to walk 900 km [km/day]k 2100 words in 50 min [words/min] l 4 kg of seed for 200 m2 [g/m2]m $5.40 for 6 min [$/min] n 100 m in 15 s [m/s]o 20 L in 1 min [mL/s] p 550 km on 50 L [km/L]

2 Sam earns $180 for an 8-hour day.a Express this as a rate ($/hour). b How much would he earn in a 35-hour week?c How long will it take him to earn $2700?

3 An 8 kg side of beef costs $22.a Express this as a rate ($/kg). b How much would 6 kg cost?c How many kilograms can be bought for $4?

4 In Sydney 52 mm of rain fell in a 16-day period, while in Melbourne 75 mm of rain fell in a 25-day period. In which city was the average rate of rainfall greater?

5 A Boeing 747 uses 7000 litres of aviation fuel in hours.a What is the fuel consumption rate (in L/h)?b How much fuel is used in 2 hours?

6 Bounta washes 15 cars in 6 h 15 min.a How long does it take him to wash one car?b At this rate how long will it take Bounta to wash 11 cars?

7 A truck maintains an average speed of 65 km/h. Calculate how far it will travel:

a in 1 h b in h c from 6:00am to 1:30pm.

8 An overnight bus travels 680 km in 8 hours. What was the average speed of the trip?

9 Magda drives her car 780 km at an average speed of 65 km/h.a How long will she take to complete the journey?b If she takes 10 hours for the return journey, calculate the average speed for the whole trip.

10 David claims 5 kg of Greenie grass seed will plant an area of 1200 m2. How much grass seed is needed for:a an area of 60 m2? b a square park of side length 0.6 km?

11 Pat and Stephen travel 750 km on the XPT train from Sydney to Albury.a The train leaves at 3:30pm and travels at an average speed of 85 km/h for the first 3 hours.

i How far has it travelled? ii What distance remains to be travelled?b How long does the XPT take to finish the trip if it averages 90 km/h for the remainder of

the journey?c What time does the XPT arrive in Albury?

12 Indonesia has a population of 231 million with a population density of about 121 persons/km2.a Estimate the area of Indonesia.b Australia’s population density is about 2.6 persons/km2 and its population is about 20 million.

If Australia was as densely populated as Indonesia, what would our population be?

312---

212---


Example 10

CAS 3-01

Sampling rates



13 The exchange rate table below shows how much the Australian dollar ($A1) is worth in other currencies.

a Cassie is planning a holiday in New Zealand with $A2000 as spending money. Convert this to New Zealand dollars.

b Chuck is visiting Australia for a business conference. If he has $US3500, how many Australian dollars (to the nearest dollar) will he receive in exchange?

c Convert each of the following.i $A100 to $US

ii $A100 to Fiji dollarsiii $A350 to yeniv $A1000 to bahtv $A648 to peso

vi $A1 million to eurosd David and Pat buy a stereo in Malaysia for $500 ringgit. How much have they paid in

Australian dollars (to the nearest dollar)?e Convert each of the following to Australian dollars, giving your answers correct to the

nearest cent.i $US1 ii £1 sterling

iii 100 peso iv 200 rupeev 500 euros vi 1000 yen

USA $0.7618 US Malaysia 2.90 ringgit

Japan 80.44 yen UK £0.42 sterling

Fiji 1.29 F Philippines 42.79 peso

India 34.53 rupee Thailand 29.82 baht

Euro 0.61 New Zealand $1.18 NZ

Currency conversionSpreadsheets can be used to convert Australian dollars to other currencies.

Step 1: Set up your spreadsheet as shown:

Step 2: Enter the names of the countries in cells A3, A4, …

Step 3: Enter the Australian dollars to be converted to the other currencies in cells C3, C4, …

Step 4: Enter the exchange rates in cell B3, B4, …

Step 5: To calculate D4, D5, …, fill down from D3.

Step 6: At the end of each question, print out your results and paste them into your workbook.

A B C D

1 Converting Australian dollars to other currencies

2 Country Exchange rate ($A1 =) $A Amount (other currency)

3 =B3*C3

4

…

Using technology

Spreadsheet



Some special ratesMost rates are reduced to a unit rate, but sometimes rates are more conveniently given in terms of 100 or 1000.

Examples of some special rates include:• fuel consumption, in litres per 100 km• birth and death rates in births or deaths per 1000 persons.

1 Use the exchange rates in the following table to convert $A1500 to the other currencies by entering the data in the appropriate cells in your spreadsheet.

2 Set up another spreadsheet to convert the following foreign currencies to $A.a 1500 euros b $NZ 1500c £800 sterling d 3000 ringgite 15 000 yen f 200 000 rupiahg 5500 baht h $US750i 148 euros j $19 000 S

Canada $1.06 Can Malaysia 2.90 ringgit

France 0.61 euros NZ $1.18 NZ

Germany 0.61 euros Singapore $1.29 S

Hong Kong $5.93 HK Switzerland 0.95 franc

Indonesia 6450 rupiah Thailand 29.82 baht

Italy 0.61 euros UK £0.42 sterling

Japan 80.44 yen USA $0.7618 US

Example 11

A car uses 32 L of petrol to travel a distance of 358 km. Calculate:a the fuel consumption in L/100 km (correct to two decimal places)b the amount of petrol used to travel 860 km.

Solutiona Fuel consumption = 32 L per 358 km

= L/1 km

= × 100 L/100 km

= 8.9385… L/100 km≈ 8.94 L/100 km

b Amount of petrol used = × 8.94

= 76.884 L (≈ 77 L)

A city’s birthrate is 15 births/1000 people. What was the city’s population if there were 450 births last year?

32358---------

32358---------

860100---------

Example 12



SolutionLet N be the city’s population.

∴ = (writing as equivalent fractions)

= (rewriting the equation with N in the numerator)

= (multiplying both sides by 450)

N = 30 000∴ The population of the city was 30 000.

151000------------ 450

N---------

N450--------- 1000

15------------

N450--------- 450×

1 1

100015

------------ 450×

Knots and nautical milesAircraft speeds are sometimes expressed in knots. The speed of a ship or yacht is usually given in knots. Wind speed may also be expressed in knots. A knot is a speed of 1 nautical mile (1852 metres) per hour, so a rate of 1 knot is a speed of 1.852 km/h.

In the early days of navigation, the method of measuring a sailing ship’s speed was to throw overboard a log with a rope tied to it. This rope had knots in it at fixed intervals. As the rope passed through his hands, a sailor counted the knots, and a simple calculation gave him the speed of the vessel, for example 15 knots.

How far would a ship sail in a day if it travelled at a speed of 20 knots? Answer in nautical miles and convert this to kilometres.

Just for the record

1 Calculate the fuel consumption, in L/100 km, of vehicles that consume:a 28 L for 200 km b 60 L for 800 km c 5.5 L for 50 kmd 20 L for 250 km e 294 L for 2400 km f 48 L for 375 kmg 40 L for 320 km h 3 L for 30 km i 35 L for 750 km

2 A car’s petrol usage is 12 L per100 km. Find how far it would travel on:a 60 L b 6 Lc 18 L d 3 Le 5.75 L (correct to one decimal place) f 1 L (correct to one decimal place)

3 A car’s fuel consumption is 10.4 L/100 km. Calculate how much fuel it will use for a trip of:a 650 km b 380 km c 1470 kmd 66 km e 2.5 km f 750 km

4 A car’s fuel consumption varies depending on how and where it is driven. A couple finds that their car uses petrol at a rate of 15 L/100 km for city driving but only 12 L/100 km for highway driving. They plan to use the long weekend to visit friends, and estimate the round trip to be 50 km of city driving and 450 km of highway driving.a How much petrol will they use for the trip?b If petrol costs an average of 109.9c/L, how much does the trip cost?




Converting ratesIt is often necessary to convert rates from one set of units to another (for example to change kilometres/hour to metres/second, or to change from millilitres/minute to litres/day).

5 For each of the following, calculate the required birthrate or deathrate per thousand people.a 3 births for 3000 people b 5 births for 2000 peoplec 52 deaths for 4000 people d 0.9 deaths for 750 peoplee 8.5 births for 250 people f 450 deaths for 100 000 people

6 Australia’s annual birthrate is approximately 12 per 1000 and the death rate is approximately 6.5 per 1000. If the population of Australia is about 20 million, calculate:a how many births occur each yearb how many deaths occur each yearc the rate of natural increase of population (birth rate minus death rate).

7 John’s V-8 car looks and sounds impressive but its petrol consumption is 18 L/100 km. Ken’s zippy 4-cylinder car only consumes petrol at a rate of 8 L/100 km. Both drive from Sydney to Melbourne and back, a distance of 1800 km. How much petrol does each car use?

Example 12

Example 13

1 Convert 60 km/h to m/s.

Solution60 km/h = 60 × 1000 m/h (1000 m in 1 km)

= 60 000 m/h

= (3600 s in 1 hour)

= m/s

= m/s

2 Change 5 m/s to km/h.

Solution5 m/s = 5 × 3600 m/h (3600 s in 1 hour)

= 18 000 m/h

= km/h (1000 m in 1 km)

= 18 km/h

3 Convert 15 mL/s to L/h.

Solution5 mL/s = 15 × 3600 mL/h (3600 s in 1 hour)

= 54 000 mL/h

= L/h (1000 mL in 1 L)

= 54 L/h

60 000 m3600 s

----------------------

60 0003600

----------------

16.6̇

18 0001000

----------------

54 0001000

----------------

Worksheet 3-07

Rates problems

Worksheet 3-08

Speed problems

STAGE5.2



Travel graphsAnother way of comparing two different quantities is to use a graph. Travel graphs are line graphs that give us information about a journey. They usually show how the quantities distance and time are related.

1 Convert:a 70 km/h to m/min b 300 km/h to m/minc 80 km/h to m/s d 95 km/h to m/se 110 km/h to m/s f 60 km/h to m/ming 40 m/s to m/min h 30 m/min to km/hi 25 m/min to km/h j 70 m/s to km/hk 2 m/s to km/h l 10 m/s to km/h

2 Convert each of these rates:a 5 kg/m to g/cm b 3 t/day to kg/hc 80 L/kg to mL/g d 40 kg/km2 to g/m2

e 6 g/min to kg/day f 15 mL/s to L/hg 8 kg/min to t/day h 3 h/m3 to s/mm3

i 20 kg/m2 to g/cm2 j 75 beats/min to beats/sk 8 km/L to m/mL l 18 L/min to mL/s

3 Belinda jogs at 2.5 m/s.a How far will she jog in 30 min?b What is her speed in km/h?

4 A car’s petrol consumption is 9.9 L/100 km. How far will the car travel on a 45-litre tank of petrol?

5 The average reaction time of a driver in applying the brakes is 3 seconds. How far will a car travel in this time if its speed is 80 km/h?

6 Pedro jogs at a constant rate on a kilometre circular track at the health club. He completes a lap in 31 seconds. If he continues to jog at the same rate, find the time he takes to run 8 km.

7 If the reaction time for a driver is 0.9 seconds, how far will the car travel in this time if the speed is:a 60 km/h?b 80 km/h?c 110 km/h?

8 China’s rate of natural increase of population is approximately 1.5%. Express this rate as a figure per 1000 of the population.

9 Wonder Gal gave Superguy a 5 s head start in a 1 km race. If Wonder Gal ran at 5 km/min and Superguy ran at 3 km/min, who won the race?

10 A train 1000 m long travels through a 3 km tunnel. If 30 seconds elapse from the time the last carriage enters the tunnel until the engine emerges from the other end, find the speed of the train, in km/h.

110------

Exercise 3-07

Example 13

CAS 3-02

Converting rates

Worksheet3-09

Jane’s diary

Worksheet3-10

Travel graph stories



Example 14

Matthew drives from Sydney to his home in Berrima. Below is a graph that shows his journey.

a How far is Matthew from home when he begins his trip? At what time did he start?b When does he make his first stop?c After his first stop, Matthew heads back towards Sydney. How is this shown by the graph?d When do you think Matthew had lunch? Why?e How long did Matthew take to drive the last 60 km home?f What was the total distance travelled by Matthew?g What was Matthew’s speed from 2:00pm to 3:30pm?h At what time did Matthew arrive home?i Between what times was Matthew’s speed slowest?

Solutiona 140 km. Matthew leaves home at 8:00am.b Matthew makes his first stop at 9:30am.c The graph rises as Matthew’s distance from home increases.d Matthew had lunch at 12:30pm because that stop lasted 1 hours and it is around the time

most people have lunch.e Matthew took 1 hours to drive the last 60 km home, from 2:00pm to 3:30pm.f Total distance travelled by Matthew was 180 km.

• 60 km from 8:00am to 9:30am.• 20 km from 10:00am to 11:00am.• 40 km from 11:30am to 12:30pm.• 60 km from 2:00pm to 3:30pm.

g Speed = where distance = 60 km and time = hours between 2:00pm and 3:30pm.

∴ Matthew’s speed =

= 40 km/hh Matthew arrived home at 3:30pm.i Matthew’s speed is slowest between 10:00am and 11:00am (the graph is not as steep).

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distancetime

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60

112---

------

STAGE5.2



1 The graph shows the journey made by Cassandra, driving to her friend’s home which is in another town.

a What is the scale on the:i horizontal axis? ii vertical axis?

b At what time did Cassandra leave home?c How many stops did she make on the trip?d Where was she when she made her first stop?e How far from home was Cassandra after:

i 3 hours? ii 7 hours?f At what times was Cassandra 60 km from home? Explain your answer.g Between what times was Cassandra’s speed the greatest? Give reasons for your answer.h What was Cassandra’s speed (in km/h) from 11:30am till 2:00pm?i What was the total distance travelled by Cassandra?

2 Megan and Jane decided to go cycling one day. Their trip is shown by the graph on the right.a What does each unit

represent on the:i horizontal axis?

ii vertical axis?b How many times during

their journey were Megan and Jane 8 km from home? Describe their journey.

c At what time did they make their first stop?

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d At what time(s) did they cycle homewards?e What was their maximum distance from home on their trip?f Megan and Jane’s trip can be divided into four stages:

i 10:00am to 11:15am ii 12:30pm to 1:15pmiii 11:45am to 12:15pm iv 1:45pm to 2:45pmWhat was their speed for each of these stages?

g How does the slope of the graph indicate the speed of the cyclists?

3 Lucia and Daniel decide to go for a walk. However, just before they start, Daniel needs to finish some work. Lucia begins walking without him, knowing that he will catch up. The graph on the right shows their distance from home at different times.a At what time did Lucia begin her

walk?b How long did Daniel take to

complete his work?c At what time did Lucia and

Daniel first meet?d Do you think Daniel is walking?

Explain.e What is Lucia’s speed from:

i 7:00am to 9:00am? ii 9:15am to 10:30am?f When is Daniel walking the fastest?

4 The graph below shows the amount of petrol in Seng’s car during a long-distance trip.

a What is the scale used on the:i horizontal axis? ii vertical axis?

b How many litres of petrol did Seng have in the tank:i at the beginning of the day? ii at 10:30am?

c How much petrol was used from 7:00am till 9:00am?

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STAGE5.2



d If Seng’s car averages 6 km/L, how far did he travel in the first 2 hours?e What was his speed for the first 2 hours?f Seng stopped for lunch and also bought some petrol. How is this shown on the graph?g How much petrol did he buy altogether?h How much petrol did he use during the day?i If petrol costs 91.9 cents per litre, what was the total cost of the petrol Seng bought during

the day?j If Seng’s car averages 6 km/L, find the number of kilometres Seng travelled during the day.k Express Seng’s fuel consumption in L/100 km.

5 Michael and Denny travelled between two towns, X and Y. Their distance from X at different times is shown by the graph on the right.a How far apart are the two

towns X and Y?b How far had Michael

travelled by the time Denny passed him?

c At what time did Denny first pass Michael?

d When did they pass each other again?

e In which direction was each going when they passed each other the second time?

f What was Denny’s maximum distance from X?g Find the total distance travelled by:

i Denny ii Michaelh What was the fastest speed of:

i Denny? ii Michael?i Excluding stops, what was the average speed of:

i Denny? ii Michael?

6 Melissa and Tuan decide to travel from town P to town Q. Their distance from P is shown by the graph.a At what time does

Tuan leave town Q?b At what time does

Melissa leave town Q?

c How far is town P from town Q?

d Find:i Tuan’s speed

over the first 12 kmii Melissa’s speed over the first 12 km.

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e By what means (foot, car, bike, …) do Tuan and Melissa travel over the first 12 km? Explain.

f At what times do they meet? State whether Melissa is overtaking Tuan or not.g Describe Melissa’s speed for the remainder of the trip.h What is Tuan’s speed after his rest?i Is Tuan’s mode of transport still the same after his rest?

1 At a school, a survey was taken in three classes to find the ratio of right-handed students to left-handed students. In 10M1 the ratio was 5 : 1, in 10M2 the ratio was 3 : 2, and in 10M3 the ratio was 6 : 1. If each class has between 21 and 26 students, which class has the most left-handed students?

2 Increase 240 in each of the following ratios:a 3 : 2 b 10 : 1 c 8 : 3

3 Decrease 180 in each of the following ratios:a 2 : 3 b 1 : 2 c 3 : 20

4 In line with the consumer price index (CPI), rail fares were increased in the ratio 10 : 9.a If the old weekly ticket cost $36, what is the new price?b Calculate the percentage increase on the original price.

5 The world champion decreased the existing lap record in the ratio 59 : 61.a Find the new record if the old one was 3 min 3 s.b Calculate the percentage decrease on the original record.

6 Robbie Rabbit and Timmy Turtle had a race. Robbie ran at a speed of 10 km/h for half the distance, then 8 km/h for the other half. Timmy ran 9 km/h for the entire distance. Who won the race, Robbie or Timmy?If the race distance was d km, by how much time did the winner beat the loser?

7 Sang and Kylie both left school and found jobs which involved travelling between two cities, A and B. One day Sang was at A and needed to travel to B, while Kylie was at B and needed to travel to A. Sang left at 9:00am and drove at a speed of 70 km/h. She stopped at 11:00am for morning tea and, after half an hour, continued on her way at 70 km/h to B. She arrived at 2:15pm. Kylie left at 10:00am and stopped for a 15 minute break after travelling 105 km. At 11:45am Kylie continued her journey, driving at a speed of 65 km/h. She reached A at 3:15pm.a How far apart are the two cities A and B?b What was Sang’s speed after her 30 minute break?c Draw a travel graph to show Sang and Kylie’s journeys.d Use the graph you drew in part c to find:

i where Sang and Kylie passed each otherii at what time this occurred.

Power plus

STAGE5.2



Topic overview• Copy and compete each of the following sentences:

The things I know about ratios and rates that I didn’t know before are …I am having difficulties with …This is what I am going to do about it …In this chapter, I found the following sections of work relevant and enjoyable …

• Copy and compete this overview using the things you have learned in this chapter.

Language of mathsbirth rate compare convert death rate

distance dividing enlargement equivalent

fraction fuel consumption rate ratio

reduction scale scale drawing simplify

slope speed steepness term

time travel graph unit unitary method

1 Which relationship compares quantities of the same type that are measured in the same units?

2 What does ‘consumption’ mean when referring to fuel consumption?

3 What two quantities are being compared in fuel consumption?

4 Which method involves finding the value of one part when given the value of the whole amount or several parts?

5 What does the slope of a travel graph illustrate?

Worksheet 3-11

Ratios and rates crossword

Simplifying ratios20 : 15 = 4 : 3

Travel graphs

Rates• speed (70 km/h)• heartbeat rate (60 beats/min)• birthrate 8.4 births/1000 people• fuel consumption 7.8 L/100 km

Scale drawing• maps

• scale1 : 200

Equivalent ratios

3 : 10

15 km/h

RATIOSAND

RATES

Applying ratios

unitarymethod

division in agiven ratio

d

t



1 Simplify each of the following ratios:a 100 : 250 b 16 : 12 c 40 cm : 4 md 3 h : 40 min e 75c : $2 f 0.5 : 1.5

g 1.6 : 0.8 h : 1 i

2 Simplify each of these ratios:a 12 : 8 : 6 b 35 : 10 : 15 c 40 : 240 : 80d $2.50 : $4.50 : $3 e 750 g : 2 kg : 1.5 kg f 15 min : 30 min : 1 h

3 a The ratio of right-handed students to left-handed students in a school is 7 : 2. If there are 630 right-handed students, find the number of left-handed students.

b Solo is building a courtyard using red and brown pavers in the ratio 2 : 3. If he already has 45 brown pavers, how many red pavers should he buy?

4 a In a children’s book the ratio of picture pages to text pages is 3 : 10. If there are 208 pages in the book, how many pages of pictures are there?

b Two friends contribute $6.50 and $3.50 to buy a $10 lottery ticket. They agree to divide any winnings in the ratio of their investment. Find the size of the larger share if they win $25 000.

c Divide 600 in each of the following ratios:i 2 : 3 ii 1 : 2 : 3 iii 2 : 1 : 4 : 3

5 Express each of the following scales as a ratio in the form a : 1 or 1 : b.a 5 cm : 20 mb 8 cm : 4 mmc 10 cm : 25 md 1 mm to 10 km

6 Use the map on the right to find the distance between:a Dubbo and

Gulgongb Dubbo and

Orangec Nyngan and Coonambled Coonabarabran and Lithgow

7 The diagram on the right is the floor plan of a room, drawn to scale.a What is the length of the room?b What is the width of the room?

Chapter 3 Review

Ex 3-01

12--- 1

3--- : 3

4---

Ex 3-01

Ex 3-02

Ex 3-03

0 100Scale

kmWest Wyalong

OrangeBathurst

PenrithLithgow

Gulgong

CoonabarabranCoonamble

Nyngan Dubbo

Parkes

20015050

Ex 3-04

Ex 3-04

Scale 1 : 100

Ex 3-04

Topic testChapter 3



8 a Simplify each of these rates:i 108 km in 3 hours (km/h) ii 7.5 kg for $44.85 ($/kg)

b If $A1 = 0.61 euros and $A1 = 80.44 yen convert each of the following:i $A60 to euros ii $A500 to yen

iii 25 to $A1 iv 1500 yen to $A1

9 a Express each of the following rates as L/100 km:i 48 L for 400 km ii 258 L for 1500 km

b Express each of the following as a rate per 1000:i 42 births for 4000 people ii 64 deaths for 10 000 people

10 Convert the following:a 15 m/s to m/min b 80 km/h to m/s c 90 kg/h to kg/mind 4 mL/s to kL/day e 5.49 L/45 km to L/100 km f 9.5 L/100 km to km/Lg 120 km/h to m/s h 5 m/s to km/h

11 Giving as much detail as possible, describe the journeys shown by these travel graphs.

a b

12 Kristen needed to go to another city. Below is a travel graph for her journey.

a How far did Kristen travel to reach the other city?b What was Kristen’s speed for the first 2 hours?c At what times did she stop?d What was Kristen’s speed for the final hour of her trip?e What mode of transport do you think she used to come home? Give reasons.f i What is the total time that Kristen spent travelling (excluding stops)?

ii What was Kristen’s average speed for the whole journey (excluding stops)?

Ex 3-05

Ex 3-06

Ex 3-07

Ex 3-08

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Documents

New Century Maths 10 - Wikispaces · 88 NEW CENTURY MATHS 10: STAGES 5.1/5.2 e During the early 1990s the unemployment rate was 10% in Australia. (Compare …