The current of a river moves at 3 miles per hour. It takes a boat 3 hours to travel 12 miles upstream, against the current, and return the same distance traveling downstream, with the current. What is the boats rate in still water?

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  1. boat's speed in still water --- x mph
    against the current ----- x-3 mph
    with the current -------- x + 3 mph

    time against current = 12/(x-3)
    time with the current = 12/(x+3)

    12/(x+3) + 12/(x-3) = 3
    times (x-3)(x+3) or x^2 - 9
    12(x-3) + 12(x+3) = 3(x^2 - 9)
    12x-36 + 12x + 36 = 3x^2 - 27
    3x^2 - 24x - 27 = 0
    x^2 - 8x - 9 = 0
    (x-9)(x+1) = 0
    x = 9 or x = -1, I guess we'll reject that negative

    the boat's speed in calm water is 9 mph

    12/12 + 12/6
    = 1 + 2
    = 3hrs.

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