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Pat races at 10 miles per hour, while Kim races at 9 miles per hour. When they both ran in the same long-distance race last week, Pat finished 8 minutes ahead of Kim. What was the length of the race, in miles? Briefly describe your reasoning.

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toporc

Let the length of the race be d miles.
Race time for Pat = d/10
Race time for Kim = d/9
If we subtract 8 minutes from the time for Kim, the result will equal the time for Pat:
\(\frac{d}{10}=\frac{d}{9}-\frac{8}{60}\)
This equation simplifies to:
\(\frac{d}{10}=\frac{5d-6}{45}\)
Cross-multiplying we get:
45d = 50d -60
60 = 5d
d = 12 miles

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