# Inverse Proportion

Inverse proportion is when two quantities change opposite to one another.

As one quantity increases, the other quantity decreases.
When the two quantities are multiplied, the same constant occurs
.

A common example of inverse proportion is to calculate the time it takes to do a job with more or fewer workers.

## Example One - Painting a Wall Mural 3 talented graffiti artists can paint a wall mural in 10 hours. To paint the same mural on another wall, calculate the time it would take:
(a) 1 artist
(b) 6 artists.

(a) Multiplied constant
= 3 artists × 10 hours
= 30 man-hours

Time with 1 artist
= 30 man-hours ÷ 1 artist
= 30 hours

(b) Time with 6 artists
= 30 man-hours ÷ 6 artists
= 5 hours

## Example Two - Building a Shed

4 men can build a shed in 20 hours. Calculate how long the same shed would take to build:
(a) if there was 1 man
(b) if there were 5 men.

(a) Multiplied constant
= 4 men × 20 hours
= 80 man-hours

Time with 1 man
= 80 man-hours ÷ 1 man
= 80 hours

(b) Time with 5 men
= 80 man-hours ÷ 5 men
= 16 hours

## Question - Building a Fence

It takes 6 people 8 hours to build a fence around a farm. How long would the same fence have taken to build with 12 people? (Hint: Find the number of hours with only 1 person first.)   