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As part of her training routine for basketball, Shaylle alternates between cycling and running for exercise. She cycles at a rate of 14 mph and runs at a rate of 8 mph. If she spends 6.5 hours exercising and covers a total of 85 miles, how much time did she spend on each exercise?

  • algebra -

    let her distance covered cycling be x miles
    let her distance covered running be 85-x miles
    time cycling = x/14
    time running = (85-x)/8

    x/14 + (85-x)/8 = 6.5
    multiply by 56

    4x + 7(85-x) = 364
    4x + 595 - 7x = 364
    -3x = -231
    x = 77

    so she cycled 77 miles
    and ran 8 miles

    time cycling = 77/14 = 5.5 hrs
    time running = 8/8 = 1 hour

    total time = 6.5 hrs , checks out!

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