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.
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: [tex]\frac{d}{10}=\frac{d}{9}-\frac{8}{60}[/tex] This equation simplifies to: [tex]\frac{d}{10}=\frac{5d-6}{45}[/tex] Cross-multiplying we get: 45d = 50d -60 60 = 5d d = 12 miles
