Free Printable 9.1 Rational Apps

1.

Katherine can paint a room in 4 hours. Joe needs 6 hours to paint the same room. Which equation would you use to determine how long it takes them to paint the room if they work together?

a)

$\frac{1}{4}+\frac{1}{6}=\frac{1}{t}$

b)

$\frac{1}{4}+\frac{1}{t}=\frac{1}{6}$

c)

$\frac{1}{6}+\frac{1}{t}=\frac{1}{4}$

d)

$t=24$

2.

A plane flies 1225 miles with a tailwind in the same time it can go 1100 miles against the wind. The speed of the plane in still air is 575 miles per hour. Which equation would you use to find the speed of the wind?

a)

$\frac{1225}{575-x}=\frac{1100}{575+x}$

b)

$\frac{1225}{575+x}=\frac{1100}{575-x}$

c)

$\frac{1225}{x+575}=\frac{1100}{x-575}$

d)

$\frac{1225}{x-575}=\frac{1100}{x+575}$

3.

George can build a laptop twice as fast as Kurt. Working together, it takes them 3 hours. Which equation would you use to determine how long it will take Kurt working alone?

a)

$2t+t=3$

b)

$\frac{1}{3}+\frac{1}{6}=\frac{1}{t}$

c)

$\frac{1}{t}+\frac{1}{3}=\frac{1}{2t}$

d)

$\frac{1}{t}+\frac{1}{2t}=\frac{1}{3}$

4.

A car travels 400 km in the same time that a freight train travels 300 km. The speed of the car is 25 km/h more than the speed of the train. Find the speed of the car and the speed of the train. (Hint set fractions equal rather than adding to a set time.)

a)

$\frac{400}{x-25}=\frac{300}{x+25}$

b)

$\frac{400}{x+25}=\frac{300}{x-25}$

c)

$\frac{400}{x+25}=\frac{300}{x}$

d)

$\frac{400}{x}=\frac{300}{x+25}$

5.

Peter can mow the lawn in 40 minutes and John can mow the lawn in 60 minutes. How long will it take for them to mow the lawn together?

a)

48 minutes

b)

50 minutes

c)

24 minutes

d)

12 minutes

6.

Joan can clean the store in five hours. If Dan helps, it takes them four hours. Without help, how long would it take Dan to complete this job ?

a)

10

b)

25

c)

20

d)

15

7.

Keith and Melanie were able to reupholster furniture in three hours together. It takes Melanie five hours to do this job alone. Without help, how long would it take Keith to do this job ?

a)

5.5

b)

6.5

c)

7.5

d)

8.5

8.

Solve for v

a)

- 7/6

b)

- 9/5

c)

9/5

d)

-3

9.

Lucy and Quinn have started a car washing business. Lucy can wash a car in 3 hours. Together, Lucy and Quinn can wash a car in 1 hour. How long does it take Quinn to wash a car by herself?

a)

It takes Quinn 4 hours.

b)

It takes Quinn 2 hours.

c)

It takes Quinn 1.5 hours.

d)

I don't know. It's too cold to wash cars! *DON'T PICK THIS!*

10.

Tim can paint the football field in 8 hours. JaQuii can paint the football field in 6 hours. Damien can paint the field in 4 hours. How long does it take them to paint the field together?

a)

It will take them 24 hours.

b)

It will take them 1.8 hours.

c)

It will take them 11 hours.

d)

It will take them 2.4 hours.

11.

Catherine can paint a house in 15 hours. Dan can paint a house in 30 hours. How long will it take them working together.

a)

20 hours

b)

10 hours

c)

22 hours

d)

17 hours

9.1 Rational Apps

Total questions: 11

Worksheet time: 15mins

Similar Resources on Wayground