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An airplane flying with the wind can cover a certain distance in a = 3 hours. The return trip against the wind takes b = 4.5 hours. How fast is the plane and what is the speed of the wind, if the one-way distance is c = 720 miles?

  • algebra -

    speed of plane in no wind --- x mph
    speed of wind ---- y mph

    time with the wind = 720/(x+y) = 3
    3x + 3y = 720
    x + y = 240

    time against the wind = 720/(x-y) = 4
    4x - 4y = 720
    x-y = 180

    add the two simplified equations:
    2x = 420
    x = 210
    back in x+y=240
    210 + y = 240
    y = 30

    the plane has a speed of 210 mph, and the wind was 30 mph

  • algebra -

    You are smart! Thanks!

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