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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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