onesun0000
Junior Member
- Joined
- Dec 18, 2018
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Two athletes at the same position on a circular 4-mile race track start running. If they run in opposite directions, they meet in 12 minutes. How ever, it takes one hour for the faster runner to gain a lap if they run in the same direction. How fast, in miles per hour, does the faster athlete run?
This is the explanation to the answer provided by the book:
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Let [MATH]x[/MATH] and [MATH]y[/MATH] be the speed of the faster athlete and slower athlete in mules per hour, respectively. Two athletes meet in 12 minutes or ([MATH]\frac{1}{5} [/MATH]hr) is 4 miles. This can be written as
[MATH]\frac{x}{5}+\frac{y}{5}=4\Rightarrow x+y=20[/MATH]
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
[MATH]x-y=4[/MATH]----
The explanation continues to solving the system and eventually get [MATH]x=12.[/MATH] 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?
This is the explanation to the answer provided by the book:
---
Let [MATH]x[/MATH] and [MATH]y[/MATH] be the speed of the faster athlete and slower athlete in mules per hour, respectively. Two athletes meet in 12 minutes or ([MATH]\frac{1}{5} [/MATH]hr) is 4 miles. This can be written as
[MATH]\frac{x}{5}+\frac{y}{5}=4\Rightarrow x+y=20[/MATH]
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
[MATH]x-y=4[/MATH]----
The explanation continues to solving the system and eventually get [MATH]x=12.[/MATH] 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?