algebra

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a steamboat travels 9 miles up a river in 3 hours and returns the same distance down the river in 2 hours. find the speed of the boat in still water and the rate of the current.

  • algebra -

    speed of boat in still water --- x mph
    speed of current --- y mph

    distance up river = time (rate) = 3(x-y) = 9
    3x-3y = 9
    x-y=3
    distance down river = 2(x+y) = 9
    2x+2y=9

    multiply first by 2
    2x-2y = 6
    2x+2y = 9
    add them
    4x = 15
    x = 15/4 = 3.75 mph
    then in x-y = 3
    3.75-y = 3
    y = .75 mph

    the boat has a speed of 3.75 mph in still water, and
    the current has a speed of .75 mph

    check:
    speed with the current = 4.5
    distance = 2(4.5) = 9
    speed against current = 3
    distance = 3(3) = 9

  • algebra -

    The current of a river is 2 miles per hour. A boat travels to a point 8 miles uptream and back in a total of 3 hours. What is the speed of the boat in still water

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