# Inverse proportion

Inversely proportional

We know proportional means comparing two ratios by putting an equal sign in.

And inversely means multiply them.

**In** the book of **verse (inverse).**

Was just lots of multiplication signs.

Inversely Proportional

`xtimesy=`CONSTANT

The values `x` and `y` are inversely proportional when one quantity increases the other decreases.

**Example 1**

The length of time to paint a room is inversely proportional to the number of people painting it.

`3` people take `8` hours

`3times8=24` people hours

`4` people take `6` hours

`4times6=24` people hours

Therefore `3times8=4times6`

**Example 2**

Sometimes they don't tell you its inverse proportion but with experience, you should recognise it as this following example.

It takes 4 women 12 days to build a brick wall. How many days will it take with 10 women?

(You should recognise that with more women it takes less time to build the wall and would, therefore, be inverse proportion)

`4` women `times12` days `=10` women `times x`

Divide both sides by `10` to get `x` on its own

`(4times12)/10=(cancel10timesx)/cancel10`

`x=(4times12)/10`

`x=48/10`

`x=4.8` days

**Example 3**

A car travelling at 50 miles per hour would take 6 hours to reach its destination. If it travelled at 80 miles per hour how long would the journey take?

This question is inverse proportion because as miles an hour goes up time goes down.

`50times6=80timesx`

Divide both sides by `80` to get `x` on its own.

`(50times6)/80=(cancel80timesx)/cancel80`

`x=(5cancel0times6)/(8cancel0)`

`x=30/8=15/4`

`x=3\3/4` hours