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  $2\dfrac{1}{2}\text{ miles}$.

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 $=2\dfrac{1}{2}\text{ miles}$

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

Distance on a hill $=\dfrac{1}{3}\times 2\dfrac{1}{2}\text{ miles}$

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

Distance you run down the slope $=\dfrac{1}{2}\times \dfrac{1}{3}\times 2\dfrac{1}{2}\text{ miles}$

$=\dfrac{1}{6}\times \dfrac{2\times 2+1}{2}\text{ miles}$

$=\dfrac{1}{6}\times \dfrac{5}{2}\text{ miles}$

$=\dfrac{5}{12}\text{ miles}$

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

Therefore, the distance you run down the slope is $\dfrac{5}{12}\text{ miles}$.