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### How Far Did Each Tire Travel?

```Date: 01/01/2003 at 22:17:42
From: Linda
Subject: A tire question

A woman went on a 80,000 mile trip. By using her spare tire, she used
all her tires (including the regular four) for equal distances. How
far did each tire travel?
```

```
Date: 01/01/2003 at 22:47:35
From: Doctor Jeremiah
Subject: Re: A tire question

Hi Linda,

Each tire must travel 4/5 of the distance, because there are 5 tires
available and only 4 tires in use at a time.

Just to simplify everything, let's say that we are going 100 miles.

The first  20 miles we use tires 1, 2, 3, 4
The second 20 miles we use tires 1, 2, 3, 5
The third  20 miles we use tires 1, 2, 5, 4
The fourth 20 miles we use tires 1, 5, 3, 4
The fifth  20 miles we use tires 5, 2, 3, 4

Look at the number of times each tire goes 20 miles. Each tire is in
exactly four of the five 20 mile trips, so each tire goes 4/5 of the
total distance.

- Doctor Jeremiah, The Math Forum
http://mathforum.org/dr.math/
```
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