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Math Help - Rational Word Problem

  1. #1
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    Rational Word Problem

    The average spped of an express train is 40km/h faster than the average speed of a bus. To travel 1200km, the bus requires 50% more time than the train. Determine the average speeds of the bus and the train.

    Rough ideas

    Train = 40 + x
    Bus = x
    Bus { 1200 = (1.5t)y
    Train { 1200 = y
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  2. #2
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    Hello, Quan!

    We know this formula: . }" alt="\text{(Distance)} \:=\:\text{(Speed)} \times \text{}" />

    Since the problem compares the times of the two vehicles,

    . . we will use this variation: . \text{Time} \:=\:\frac{\text{Distance}}{\text{Speed}}


    The average spped of an express train is 40km/h faster than the average speed of a bus.
    To travel 1200km, the bus requires 50% more time than the train.
    Determine the average speeds of the bus and the train.

    Let: x = speed of bus.
    Then: x+40 = speed of train.

    The train's speed is x+40 km/hr.
    . . To travel 1200 km, it takes: \frac{1200}{x+40} hours.

    The bus' speed is x km/hr.
    . . To travel 1200 km, it takes: \frac{1200}{x} hours.

    We are told that the bus' time is 50% more than the train's time.
    . . That is, it is: 1\frac{1}{2} \:=\:\frac{3}{2} times the train's time.


    There is our equation! . . . . . \frac{1200}{x} \;=\;\frac{3}{2}\cdot\frac{1200}{x+40}


    Can you finish it now?

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