algebra

posted by allie

diana drove 320 miles, then increased her speed by 10 miles per hour for 500 miles. if the second part of the trip took 2 hours longer than the first, find her average speed.

  1. Reiny

    let her initial speed be x mph
    time for first trip = 320/x

    new speed = x+10 mph
    time for second part of trip = 500/(x+10)
    so..

    500/(x+10) - 320/x = 2
    times x(x+10)
    500x - 320(x+10) = 2x(x+10)
    500x - 320x - 3200 = 2x^2 + 20x
    2x^2 - 160x + 3200 = 0
    x^2 - 80x + 1600 = 0
    (x-40^2 = 0
    x = 40

    time for first leg = 320/40 =8 hrs
    time for 2nd leg = 500/50 = 10 hrs
    avg speed = total distance/total time
    = 820/18 = appr 45.56 mph

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