Inverse Proportion

## Inverse Proportion

For Inverse Proportion, as one value increases, the other value falls. The change in one must be at the same rate as the change in the other: if one amount doubles, then the other amount must be halved.

A typical example would involve the time taken to complete a task, and the number of people involved in that task. If the number of people on the task increased by a factor of three, then the amount of time taken to complete the task would be a third of the original time.

Multiplying one side of the proportion by a factor means multiplying the other side by the inverse of that factor.

## Example 1

An exhibition hall is being prepared. It normally takes 12 people six days to prepare the exhibition hall. However, only 8 people are available. How long will it take to prepare the hall?

12 people take six days

Because this is an inverse proportion (fewer people will take longer):

8 people is frac(2)(3) of 12

Multiply 6 days by the inverse of frac(3)(2)

= 6 x frac(3)(2) = 9

## Example 2

A car takes 5 hours for a journey at an average speed of 40mph. How long will the journey take if the average speed is 55mph? Give the answer to the nearest minute.

This is an inverse proportion; the higher the value of the speed, the smaller the value of the time.

40mph takes 60 x 5 = 300 minutes

55 mph is frac(55)(40) of 40. Simplify to frac(11)(8)

Multiply 300 minutes by the inverse = 300 x frac(8)(11) = 218.18 minutes

This is three hours and 38 minutes (nearest minute)