#### onesun0000

##### Junior Member

- Joined
- Dec 18, 2018

- Messages
- 62

This is the explanation to the answer provided by the book:

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Let \(\displaystyle x\) and \(\displaystyle y\) be the speed of the faster athlete and slower athlete in mules per hour, respectively. Two athletes meet in 12 minutes or (\(\displaystyle \frac{1}{5} \)hr) is 4 miles. This can be written as

\(\displaystyle \frac{x}{5}+\frac{y}{5}=4\Rightarrow x+y=20\)

It takes one hour for the faster athlete to gain a lap if both athletes run n the same directions, which means that the difference of the distances that they run is 4 miles. This can be written as

\(\displaystyle x-y=4\)

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The explanation continues to solving the system and eventually get \(\displaystyle x=12.\) I don't understand the part "...which means the difference of the distances they run is 4 miles...". Why is that? and why the same variables when it says those represent the speed of the two athletes?