Question

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.

Answer 1

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