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When Sarah takes the bus to work, the trip takes 30 minutes. When she takes the train to work, the trip takes 20 minutes. The average speed to the train is 15 mph faster than the speed of the bus. Find the distance to work.

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  1. speed of bus -- x mph
    speed of train -- x+15 mph

    Distance by train = (20/60)(x+15)
    distance by bus = (30/60)x
    but the distance is the same

    (1/3)(x+15) = (1/2)x
    times 6
    2(x+15) = 3x
    2x+30 = 3x
    x = 30 mph
    The bus goes at 30 mph, the train goes at 45 mph

    distance = (1/2)x = (1/2)(30) = 15 miles

    check:
    time by bus = 15/30 = .5 hr = 30 min
    time by train = 15/45 = 1/3 hr = 20 minutes

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