# 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?