# math

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It took a faster runner 10 sec. longer to run a distance of 1500 m than it took a slower runner to run a distance of 1000 m.If the rate of the faster runner was 5 m/sec more than the rate of the slower runner,what was rate of each?

• math -

Let V be the speed of the slower runner. Let his (or her) time to run 1000 m be T. The faster runner's speed is V + 5 (in meters per second). Here is what you know:
(V+5)(T+10) = 1500
V*T = 1000

V*T + 5T + 10V + 50 = 1500
5T + 10V = 450
5000/V + 10V = 450 (after substituting 1000 for V*T)

V^2 -45V + 500 = 0
(after multiplying boith sidesw by V and dividing by 10)
(V-25)(V-20) = 0

V = 20 m/s, V+5 = 25 m/s, T = 50s would be one answer
V = 25 m/s, V+5 = 30; T = 40 s would be another answer.

It sounds fishy to me that there are two possible sets of answers. The speeds are also faster than humans can run.

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