HW # 58 - Ready to Go On p. 242 # 1-20 all Warm up

HW # 58 - Ready to Go On p. 242 # 1-20 all

Warm up

Week 17, Day One

Find each unit rate.

1. jump rope 192 times in 6 minutes

2. four pounds of bananas for $2.36

3. 16 anchor bolts for $18.56

4. 288 movies on 9 shelves

32 jumps/min

$0.59/lb

$1.16/bolt

32 movies/shelf

Warm Up Response

24

Homework Checkp. 234-235 # 6-30 even and 31, 32, 336) 27.5 pounds8) 12 min10) Yes12) Yes14) 24, 7th graders16) 5 min18) ¼ and 4/1620) 49/182, 7/2622)a/b, 4a/4b24) 114 students

26) $4828) 330 miles30) 92 shirts31) About 3.2 about 68 mm Hg

32) Yes; the ratio is less than 2.82:1

33) 154 and 56

Goals for Today

• Word problems (together)

• CW:Problem Solving 5-4Challenge 5-4

The largest block of cheese on record weighted 920,136 oz. How many tons is this?

About 28.75 tons

The rate of one knot equals one nautical mile per hour. One nautical mile is 1852 meters. What is the speed in meters per second of a ship traveling at 20 knots?

About 10.3 m/s

The Outer Bay exhibit at the Monterey Bay Aquarium holds about 1,000,000 gallons of sea water. How many days would it take to fill the exhibit at a rate of 1 gallon per second? About 11.57 days

Vocabularyconversion factor

The process of converting from one unit to another is called dimensional analysis, or unit analysis. To convert units, multiply by one or more conversion factors. A conversion factor is a ratio of two quantities that are equal but use different units.

For example, to convert inches to feet

you would use the ratio as a conversion factor.1 ft12 in.

Multiplying by a conversion factor is like multiplying by 1.

12 in.12 in.

1 ft1 ft

= = = 11 ft12 in.

The average American uses 580 pounds of paper per year. Find this rate in pounds per month, to the nearest tenth.

Additional Example 1: Using Conversion Factors to Solve Problems

Convert the rate 580 pounds per year to pounds per month.

580 lb 1 yr

1 yr 12 mo

580 lb 12 mo

48.3 lb per month

To convert the second amount in a rate, multiply by the conversion factor with that unit in the first quantity.

Divide 580 by 12.The average American uses 48.3 pounds of paper per month.

Divide out like units. •yr

mo = lbmo

lb yr

Check It Out! Example 1Sam drives his car 23,040 miles per year. Find this rate in the number of miles driven per month, to the nearest mile.

Convert the rate 23,040 miles per year to miles per month.

23,040 mi 1 yr 1 yr 12 mo

23,040 mi 12 mo =

= 1920 per month Divide 23,040 by 12.

Sam drives his car 1920 miles per month.

Divide out units. •yr

mo =mimo

miyr

To convert the second amount in a rate, multiply by the conversion factor with that unit in the first quantity.

Additional Example 2: Problem Solving Application

A car traveled 60 miles on a road in 2 hours. Find this rate in feet per second.

1 Understand the Problem

The problem is stated in units of miles and hours. The question asks for the answer in units of feet and seconds. You will need to use several conversion factors.

List the important information:

• Feet to miles5280 ft

1 mi

• Hours to minutes

• Minutes to seconds1 min60 s

1 h60 min

You know the conversion factor that converts miles to feet. So multiply by each conversion factor separately, or simplify the problem and multiply by several conversion factors at once.

2 Make a Plan

Convert to miles per hour.

Solve3

60 mi2 h

= (60÷2) mi(2÷2) h

= 30 mi1 h

Create a single conversion factor to convert hours directly to seconds:

hours to seconds = • 1 min60 s

Set up the conversion factors.

minutes to seconds1 min60 shours to minutes 1 h

60 min

1 h60 min

1 h3600 s

=

30 mi1 h

• 5280 ft1 mi

• 1 h 3600 s

Solve Continued3

30 • 5280 ft • 1 1 • 1 • 3600 s = 158,400 ft

3600 s= 44 ft

1 s

The car was traveling 44 feet per second.

Divide out like units.• •30 mi1 h

5280 ft1 mi

1 h 3600 s=

=

A rate of 44 ft/s is less than 50 ft/s. A rate of 60 miles in 2 hours is 30 mi/h or 0.5 mi/min.

4 Look Back

Since 0.5 mi/min is less than 3000 ft/60 s or 50 ft/s and 44 ft/s is less than 50 ft/s, then 44 ft/s is a reasonable answer.

Check It Out! Example 2

A train traveled 180 miles on a railroad track in 4 hours. Find this rate in feet per second.

1 Understand the Problem

The problem is stated in units of miles and hours. The question asks for the answer in units of feet and seconds. You will need to use several conversion factors.

List the important information:

• Feet to miles5280 ft

1 mi

• Hours to minutes

• Minutes to seconds1 min60 s

1 h60 min

2 Make a Plan

You know the conversion factor that converts miles to feet. So multiply by each conversion factor separately, or simplify the problem and multiply by several conversion factors at once.

First, convert 180 miles in 4 hours into a unit rate.Solve3

180 mi4 h

= (180 ÷ 4) mi(4 ÷ 4) h

= 45 mi1 h

Create a single conversion factor to convert hours directly to seconds:

hours to seconds = • 1 min60 s

Set up the conversion factors.

minutes to seconds1 min60 shours to minutes 1 h

60 min

1 h60 min

1 h3600 s

=

45 mi1 h

• 5280 ft1 mi

• 1 h 3600 s

Solve Continued3

45 • 5280 ft • 1 1 • 1 • 3600 s = 237,600 ft

3600 s= 66 ft

1 s

The train was traveling 66 feet per second.

Divide out like units.• •45 mi1 h

5280 ft1 mi

1 h 3600 s=

=

A rate of 66 ft/s is more than 50 ft/s. A rate of 180 miles in 4 hours is 45 mi/h or 0.75 mi/min.

4 Look Back

Since 0.75 mi/min is more than 3000 ft/60 s or 50 ft/s and 66 ft/s is more than 50 ft/s, then 66 ft/s is a reasonable answer.

Additional Example 3: Physical Science ApplicationA strobe lamp can be used to measure the speed of an object. The lamp flashes every of a second. A camera records the object moving 52 cm between flashes. How fast is the object moving in m/s? Use dimensional analysis to check the reasonableness of your answer.

1 100

distance .time

Use rate =52 cm

1100 s

It may help to eliminate the fraction first.

Additional Example 3 Continued

1 100

Multiply numerator and denominator by 100.

5200 cm1 s

=

52 cm1

100 s

= 100 • 52 cm 1

100 s 100 •

Convert centimeters to meters to see if the answer is reasonable.

Additional Example 3 Continued

5200 cm1 s

Multiply by the conversion factor.

5200 m100 s=

52 m1 s =

The object is traveling 52 m/s.

5200 cm1 s

= •1 m

100 cm

Check It Out! Example 3

A strobe lamp can be used to measure the speed of an object. The lamp flashes every of a second. A camera records the object moving 65 cm between flashes. How fast is the object moving in m/s?

1 100

distance .time

Use rate =65 cm1

100 s

It may help to eliminate the fraction first.

Check It Out! Example 3 Continued

1 100

Multiply numerator and denominator by 100.

6500 cm1 s

=

65 cm1

100 s

= 100 • 65 cm 1

100 s 100 •

Convert centimeters to meters to see if the answer is reasonable.

Check It Out! Example 3 Continued

6500 cm1 s

Multiply by the conversion factor.

6500 m100 s=

65 m1 s =

The object is traveling 65 m/s.

6500 cm1 s

= •1 m

100 cm

Lesson Quiz

1. You drive 136 miles from your house to your aunt’s house at the lake. You use 8 gallons of gas. How many yards does your car get to the gallon?

2. A cheetah was timed running 200 yards in 6 seconds. What was its average speed in miles per hour?

29,920 ydgal

≈ 68 mi/h