Word Problems

Homework

With a tailwind, a helicopter flies 270 miles in 1.5 hours. When the helicopter flies back against the same wind, the trip takes 3 hours. What is the helicopter’s speed in still air? What is the speed of the wind?

Withthe wind

270

Rate Time Distance

Againstthe wind

1.5h w h w 1.5 270

h w 3 270 2703h w

w = speed of wind (mph) h = speed of the helicopter (mph)

#1

Homework

#1 With a tailwind, a helicopter flies 270 miles in 1.5 hours. When the helicopter flies back against the same wind, the trip takes 3 hours. What is the helicopter’s speed in still air? What is the speed of the wind?

h w 1.5 270

h w 3 270

w = speed of wind (mph) h = speed of the helicopter (mph)

h w 180

h w 90 2h 270h 135w 45

Helicopter = 135 mph

Wind = 45 mph

Homework

#2 A barge on the Sacramento river travels 24 miles upstream in 3 hours. The return trip take the barge only two hours. Find the speed of the barge in still water.

Withthe current

24

Rate Time Distance

Againstthe current

2b c b c 2 24

b c 3 24 243b c

b = speed of barge (mph) c = speed of the current (mph)

Homework

b c 12

b c 8

2b 20b 10c 2

barge = 10 mph

current = 2 mph

#2 A barge on the Sacramento river travels 24 miles upstream in 3 hours. The return trip take the barge only two hours. Find the speed of the barge in still water.

b = speed of barge (mph) c = speed of the current (mph)

b c 2 24

b c 3 24

Homework

Bubba has a collection of 95 coins, consisting of only nickels, dimes and quarters. If the number of quarters and dimes combined is 60, and the total value of all his coins is $12.70, how many dimes does he have?

d = number of dimesq = number of quarters

Define variables:

d q 60 Write two equations

E1

E2

Number of nickels = 35

Value of nickels = $1.75

Value of dimes and quarters = $10.95

25d 25q 1500

15d 405 d 27

27 dimes

#3

10d 25q 1095

Homework

#1 The length of a rectangle is three more than it’s width. If the perimeter is 66 meters, find the area of the rectangle.

L = length

W = width

Define variables: Write two equations

E1

E2

L W 3 2L 2W 66

2 2 63 6W W E1 E2

2W 6 2W 66 4W 60W 15L 18

2270 m

1n n4 4 3

The numerator of a fraction is one less than the denominator. If 1 is subtracted from the numerator, and the denominator is unchanged, the resulting fraction has a value of 3/4. Find the original fraction.

d n 1 n = Numerator

d = Denominator

Define variables:

Extra Credit Problem

Write two equations

E1

E2

n 1n 1d 3

4

4 n 1 3d

4n 4 3d

4n 4 3d E1 E2

4n 4 3n 3 n 7 d 8

78

From homework on 12/12