# 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.

Answer:
(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.

Answer:
(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.)

Answer
4 hours

## Maths Fun - BMI (Body Mass Index)

Doctors use a Body Mass Index to determine if people are healthy or not. A BMI of 25 is healthy. Less than 25 is underweight. More than 25 is overweight.

 Body Mass Index = Mass in kg Height in metres-squared

Measure your mass in kilograms. Measure your height in metres. Calculate your BMI.
According to the rule above, are you healthy? What problems are there with this rule?   