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Math Help - Plane distance problem

  1. #1
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    Plane distance problem

    An airplane was supposed to cover the distance of 2900 km. However, after covering 1700 km, it had to land and wait on the ground for 1 hours and 30 minutes. After it took off again, its average speed was 50 km/h less than before. Find the original average speed of the plane if it is known that it completed the flight five hours after departure. help would be appreciated thanks!
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  2. #2
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    Hello, jarny!

    An airplane was supposed to cover the distance of 2900 km.
    However, after covering 1700 km, it had to land and wait on the ground for 1 hours and 30 minutes.
    After it took off again, its average speed was 50 km/h less than before.
    Find the original average speed of the plane if it completed the flight 5 hours after departure.

    Let x = original speed of the plane (km/hr).

    It flew 1700 km at x km/hr.
    . . This took: .1700/x hours.

    It flew the remaining 1200 km at (x - 50) km/hr.
    . . This took: .1200/(x - 50) hours.

    The plane flew a total of 3 hours.

    . . And there is our equation: .1700/x + 1200/(x - 50) .= .7/2


    Multiply through by 2x(x - 50): .3400(x - 50) + 2400x .= .7x(x - 50)


    This simplifes to the quadratic: .7x - 6150x + 170,000 .= .0

    . . which factors: .(x - 850)(7x - 200) .= .0

    . . and has roots: .x .= /850, 200/7


    We reject the smaller root: x = 200/7
    At about 28.6 km/hr, it would take over 100 hours to fly 2900 km.

    Therefore, the original speed of the plane was: 850 km/hr.

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