6th Grade Math Textbook, Fundamentals

Lesson 6-9 for exercise sets. &KDSWHU 

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Write and solve an inverse proportion to solve each problem.

1.If Cora drives at the rate of 50 miles per hour, it takes her 1 hours to

make a 75-mile trip. How long does the trip take if she drives at a rate

of 40 miles per hour?

2.Discuss and Write Explain why the car-wash problem on page 164 is

an inverse proportion. Make a table to support your answer.

1

2

As with direct proportion problems, you can use either like or unlike units

for each ratio when solving inverse proportion problems.

Hilda walks 3 miles on her treadmill every morning.

At the rate of 3 miles per hour, it takes her an hour to

walk that distance on the treadmill. If she increases her

rate of speed to 4 miles per hour, how long will it take

her to walk the same 3 miles?

Let hthe number of hours Hilda will walk at a rate

of 4 miles per hour.

Method 1 Use LikeUnits for Each Ratio

more time on treadmillless time on treadmill 3 mi/h4 mi/h 1 hourh

fewer miles per hour

more miles per hour

Think

As the rate of speed

increases,the amount

of time on the treadmill

decreases.

Solve: 

 Cross multiply.

3  4 h

3  4  4 h 4 Divide both sides by 4 to isolate h.

h

Method 2 Use UnlikeUnits for Each Ratio



Solve: 

 Cross multiply.

3  4 h

3  4  4 h 4 Divide both sides by 4 to isolate h.

h

So it will take Hilda hour to walk 3 miles at a rate of 4 miles per hour.^34

4

1

3

h

4 mi/h

1 hour

3 mi/h

h

more miles per hour

more time on treadmill

fewer miles per hour

less time on treadmill

3

4

4

1

3

h

h

1

3

4

3

4

h

1

3

4

Check: Substitute for h.

3 • 1 • 4 Cross multiply.

3  3 Tr u e

3

4

3

3

4

4

1

?

?^3

4

Check: Substitute for h.

3 • 1 4 • Cross multiply.

3  3 Tr u e

3

4

?

(^3) ?
4
3
4
1
3
4