Question

A man drove 15/4 miles from his home to his office. He then went out for lunch to a nearby restaurant 2/3 miles from his office and back. Later on he goes to a store 2 miles from his office and then drove back to his home 11/6 miles. What distance in total did he travel?

Answer 1

Let's get all of the distances lined up:

$\frac{15}{4}$ = home to office
$\frac{2}{3}$ to a restaurant
$\frac{2}{3}$ back to the office
$2$ = store
$\frac{11}{6}$ = back home

So then we just add up all of the numbers. However we need to make sure that there is a common denominator. Let's make the common denominator 12, since that is a common factor to all of the denominators in the problem:

$\frac{45}{12}$ = home to office
$\frac{8}{12}$ to a restaurant
$\frac{8}{12}$ back to the office
$\frac{24}{12}$ = store
$\frac{22}{12}$ = back home

Then let's add them up:

$\frac{45}{12} + \frac{8}{12}+ \frac{8}{12}+ \frac{24}{12}+ \frac{22}{12}= \frac{107}{12} miles$

This does not reduce to a nice number, however, we can simplify to:

$8 \frac{11}{12}miles$