SOLUTION: One runner finishes a race in one hour. A second runner finishes 20 minutes later. If the rate of the faster runner is 2 mph more than the rate of the slower, find the rate of each

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Question 573269: One runner finishes a race in one hour. A second runner finishes 20 minutes later. If the rate of the faster runner is 2 mph more than the rate of the slower, find the rate of each runner.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
One runner finishes a race in one hour.
A second runner finishes 20 minutes later.
If the rate of the faster runner is 2 mph more than the rate of the slower, find the rate of each runner.
:
let r = the rate of slower runner
then
(r+2) = the rate of the faster
:
Convert 1 hr 20 min to 4%2F3 hr, (the time of the slower runner
:
We know they both ran the same distance, write a dist equation
dist = time * speed
:
1(r+2) = 4%2F3r
Multiply both sides by 3
3(r+2) = 4r
3r + 6 = 4r
6 = 4r - 3r
r = 6 mph is the rate of the slower runner
then, obviously:
8 mph = the rate of the faster runner
:
:
Find the distances, if we did this right, they should be equal
1*8 = 8mi
4%2F3*6 = 8 mi