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30 April, 16:50

The average speed of an airplane is four times as fast as the average speed of a passenger train. To travel 1440 km, the train requires 12 h more than the airplane. Determine the average speeds of the train and the airplane.

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  1. 30 April, 17:01
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    Answer

    Average speed of the train = 90 km/h and average speed of the airplane = 360 km/h.

    Explanation:-

    If speed of train = x then the speed of airplane = 4x km/h and we have the 2 equations

    x = 1440 / (t + 12) (t = time taken by the train)

    4x = 1440 / t ... (1) (t = time taken by train)

    Multiply the first equation by 4:-

    4x = 5760 / (t + 12) ... (2)

    Combining equations (1) and (2) : -

    1440 / t = 5760 / (t + 12)

    Cross multiplying:-

    5760t = 1440t + 17,280

    4320t = 17,280

    t = 17280/4320

    t = 4 hours

    speed of train = 1440 / (4 + 12) = 90 km/h and speed of plane = 4*90 = 360 km/h.
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