SOLUTION: A high school track coach determines that his fastest long distance runner runs 2 miles per hour faster than his slowest runner. Compared to the faster runner, the slower runner ta

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: A high school track coach determines that his fastest long distance runner runs 2 miles per hour faster than his slowest runner. Compared to the faster runner, the slower runner ta      Log On


   

Question 613389: A high school track coach determines that his fastest long distance runner runs 2 miles per hour faster than his slowest runner. Compared to the faster runner, the slower runner takes a half hour longer to run 12 miles.
a. Find the average rates of both runners.
b. Find the time for both runners to run 12 miles.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A high school track coach determines that his fastest long distance runner runs 2 miles per hour faster than his slowest runner.
Compared to the faster runner, the slower runner takes a half hour longer to run 12 miles.
:
a. Find the average rates of both runners.
Let s = speed of the slower runner
then
(s+2) = speed of the faster runner
:
Write a time equation; time = dist/speed
12%2Fs - 12%2F%28%28s%2B2%29%29 = .5 hr
Multiply s(s+2), results:
12(s+2) - 12s = .5s(s+2)
12s + 24 - 12s = .5s^2 + s
0 = .5s^2 + s - 24
multiply by 2, to get rid of the decimal
s^2 + 2s - 48 = 0
Factors to
(s+8)(s-6) = 0
The positive solution
s = 6 mph the slow runner
then
6 + 2 = 8 mph is the faster runner
:
:
b. Find the time for both runners to run 12 miles.
12/8 = 1.5 hrs the faster runner
12/6 = 2 hrs the slower