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The road connecting two mountain villages goes only uphill or downhill. A bus always travels 15 mph uphill and 30 mph downhill. Find the distance between the villages if it takes exactly four hours for the bus to complete a round trip.

  • Math -

    I always had my students do these questions by organizing the information in a chart.
    let the time take to go uphill be t hours
    then the time taken to go downhill is 4-t hours

    .......... Dist.....rate..time
    uphill: ....15t......15....t
    downhill....30(4-t) ..30...4-t

    (I hope this somehow lined up)

    but the distance is the same, so

    15t = 30(4-t)
    15t = 120 - 30t
    45t = 120
    t = 8/3

    distance = 15t = 15(8/3)
    = 40 km

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