# Worksheet: Inverse Variation and Its Applications

In this worksheet, we will practice applying inverse variation to write an equation to describe it and to use proportions to find other sets of values.

**Q3: **

Given that varies inversely with , and when , write an equation for in terms of .

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- B
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- E

**Q4: **

Which of the following relations represents an inverse variation between the two variables and ?

- A
- B
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- D

**Q5: **

The rate of vibration of a string under constant tension varies inversely with the length of the string. If a string is 24 inches long and vibrates 128 times per second, what is the length of a string that vibrates 64 times per second?

**Q6: **

A group of scouts receives a donation of to fund places on an international jamboree. The amount each scout receives for their trip varies inversely with the number of scouts from the group going to the jamboree.

Write an equation for , the amount each scout receives, in terms of , the number of scouts from the group who are going to the jamboree.

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If 25 scouts from the group are going to the jamboree, how much will each scout receive from the donation?

**Q7: **

Suppose that is inversely proportional to and that when . Write the equation, giving in terms of .

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**Q8: **

A copy center is printing leaflets for a local school. The time it takes for the job to be completed varies inversely with the number of copiers used, and if 4 copiers are used, the job will take of an hour.

How many copiers are required to complete the job in half an hour?

Letting be the time in hours to complete the job using copiers, what is the value of the product, ?

Write an equation for in terms of .

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**Q9: **

Community groups have been invited to apply for a grant from a fund. The amount a group will receive varies inversely with the number of successful applications.

If there are 45 successful applications, each group will receive $800.

How much will each group receive if there are 360 successful applications?

How many successful applications mean that each group receives ?

How much will each group receive if there are 150 successful applications?

What is the total value of the fund?

Write an equation for , the number of dollars each group receives when groups make successful applications.

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**Q12: **

A building contractor is constructing part of the perimeter wall for a school. The wall will be the same height all along its length. The length of time it will take to build the wall varies inversely with the number of bricklayers. A team of 12 bricklayers is expected to take 30 days to build the wall.

Write an equation for the number of days, , it would take a team of bricklayers to build the wall.

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How many bricklayers are required if the wall is to be finished in 20 days?

**Q13: **

Farida buys 5 litres of juice to share between the children at a party. The amount of juice each child will receive varies inversely with the number of children at the party. Write an equation for , the amount of juice in millilitres each child will receive, in terms of , the number of children at the party.

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**Q14: **

The time taken to complete a car journey at a steady speed varies inversely with the speed of the car.

Most of the quickest route from Josephβs Corner to Round Rock is on the I-35. At 45 mph, this part of the journey takes 2 hours and 40 minutes.

How long would the journey take at 75 mph?

- A 1 hour and 55 minutes
- B 1 hour and 15 minutes
- C 2 hours and 15 minutes
- D 1 hour and 36 minutes
- E 2 hours and 36 minutes

Write an equation for , the time it takes to cover this part of the journey at speed .

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- B
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How much of the route is on the I-35?

**Q15: **

If , , and when , find when .

- A
- B 16
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- D

**Q16: **

Determine the correct relation from the following choices, given that , , and .

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- D

**Q17: **

Given that , where varies inversely with , and when , determine the value of when .

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**Q18: **

If , , and when , which of these equations represents the relation between and .

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**Q19: **

The height of a right circular cylinder varies inversely with the square of its radius . If when , determine when .

**Q20: **

Given that , and when , find when .

**Q21: **

The speed, , of water spraying from the end of a garden hose varies inversely with the square of the hose nozzle radius, . If cm/s when cm/s, find when cm/s.

**Q22: **

If , and when , find the value of when .

**Q23: **

Given that varies inversely with , and when , find the value of when .

**Q24: **

Given that , where varies inversely with , and when , find the relation between and .

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**Q25: **

A company making footballs decided to cut the selling price of each football by . Assuming all their footballs are identical and the same price, if they wanted to get the same amount of money from sales, by what percentage will they need to increase the number of footballs sold? Round your answer to the nearest whole number.