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March 24, 2017

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A plane flies 460 miles with the wind and 310 miles against the wind in the same length of time. If the speed of the wind is 30 mph, what is the speed of the plane in calm air?

  • College Math - ,

    speed of plane in calm air --- x mph

    time to go 460 miles with the wind = 460/(x+30)
    time to go 310 miles against the wind = 310/(x-30)

    they are equal, so
    460/(x+30) = 310/(x-30)
    460(x-30) = 310(x+30)
    460x - 13800 = 210x + 9300
    150x = 23100
    x = 154

    the speed of the plane is 154 mph

    check:
    speed with the wind = 184
    time of trip against wind = 460/184 = 2.5 hours
    speed against wind = 124 mph
    time of trip against wind = 310/124 = 2.5 hours.

    My answer is correct.

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