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18 September, 07:23

A canoe travels on a river whose current is running at 6 miles per hour. After traveling 175 miles upstream, the canoe turns around and makes the 175 -mile trip back downstream. The trip up and back takes 10 hours. What is the speed of the canoe in still water?

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  1. 18 September, 07:31
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    The speed going up stream is x - 6

    The speed going downstream is x + 6

    SO to find how long you take going upstream is 175 / (x - 6)

    Downstream is 175 / (x + 6)

    Add those 2 fractions together and get a total of 10

    175 / (x - 6) + 175 / (x + 6) = 10

    175 (x - 6) + 175 (x + 6) = 10 (x - 6) (x + 6)

    175x - 175 (6) + 175x + 175 (6) = 10 (x^2 - 36)

    350x = 10x^2 - 360

    10x^2 - 350x - 360 = 0

    x^2 - 35x - 36 = 0 - I saw that 10 will divide out to make my life easier

    (x - 36) (x + 1) = 0

    x - 36 = 0 x + 1 = 0

    x = 36 x = - 1 (Throw this one out)

    The canoe travels 36 miles per hour in still water
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