Racing long distance

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?

Answer 1

Ellie,

 

The length, L = speed*time

 

10(t) = 9(t+8/60)     //They run the same length L.

 

10t = 9t + 72

 

t = 1.2 hour

 

Length = 10(1.2) = 12 miles = 9(1.2+8/60)

Answer 2

After the first hr, Pat is ahead by one mile, which takes Kim an extra 6.67 minutes. So now you know it has to be a little longer than 10 miles, because Pat runs 10 miles 60 minutes, and Kim runs 10 miles in 1.1hrs or 67 minutes -- a difference of almost 7 minutes

 

If the race is 12 miles long, it takes Pat 1.2 hours, or one hr and 12 minutes. Kim runs it in 12 miles/9mph or 1.3 hours or 1 hr 20 mins. The difference is 8 minutes.

 

12 miles divided by 10 mph for Pat

12 miles divided by 9 mph for Kim

 

to solve the problem start with the most simple assumption that they run for one hour and calculate the difference in time to give you a CLUE as to how you will proceed. If you cannot think of an algebraic method or equation, simplify the process of problem solving, break it down into a simpler set of statements