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:


`(15)/(4)` = home to office

`(2)/(3)` to a restaurant

`(2)/(3)` back to the office

`2` = store

`(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:


`(45)/(12)` = home to office

`(8)/(12)` to a restaurant

`(8)/(12)` back to the office

`(24)/(12)` = store

`(22)/(12)` = back home

Then let's add them up:


`(45)/(12) + (8)/(12)+ (8)/(12)+ (24)/(12)+ (22)/(12)= (107)/(12) miles`

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


`8 (11)/(12)miles`