Question

You run 2 1/2 miles as a part of an exercise routine. You run 1/3 of that distance on a hill. You run down a slope for the last 1/2 of the hill. On how many miles of your run do you run down the slope? Write your answer as a fraction or mixed number in simplest form.

Answer 1

Given:

Total distance for daily exercise is
`2(1)/(2)\text{ miles}`.

You run 1/3 of that distance on a hill.

You run down a slope for the last 1/2 of the hill.

To find:

The distance you run down the slope.

Solution:

We have,

Total distance
`=2(1)/(2)\text{ miles}`

You run 1/3 of that distance on a hill.

Distance on a hill
`=(1)/(3)* 2(1)/(2)\text{ miles}`

You run down a slope for the last 1/2 of the hill.

Distance you run down the slope
`=(1)/(2)* (1)/(3)* 2(1)/(2)\text{ miles}`

`=(1)/(6)* (2* 2+1)/(2)\text{ miles}`

`=(1)/(6)* (5)/(2)\text{ miles}`

`=(5)/(12)\text{ miles}`

In cannot be expressed as mixed fraction because 5<12.

Therefore, the distance you run down the slope is
`(5)/(12)\text{ miles}`.