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29 November, 13:12

In still water, a boat averages 18 18 miles per hour. it takes the same amount of time to travel 16 miles 16 miles downstream, with the current, as it does 8 8 miles upstream, against the current. what is the rate of the water's current?

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  1. 29 November, 16:44
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    The current is 6 miles per hour.

    Let's create a few equations:

    Traveling with the current:

    (18 + c) * t = 16

    Traveling against the current:

    (18 - c) * t = 8

    Let's multiply the 2nd equation by 2

    (18 - c) * t*2 = 16

    Now subtract the 1st equation from the equation we just doubled.

    (18 - c) * t*2 = 16

    (18 + c) * t = 16

    (18 - c) * t*2 - (18 + c) * t = 0

    Divide both sides by t

    (18 - c) * 2 - (18 + c) = 0

    Now solve for c

    (18 - c) * 2 - (18 + c) = 0

    36 - 2c - 18 - c = 0

    36 - 2c - 18 - c = 0

    18 - 3c = 0

    18 = 3c

    6 = c

    So the current is 6 mph.

    Let's verify that.

    (18 + 6) * t = 16

    24*t = 16

    t = 16/24 = 2/3

    (18 - 6) * t = 8

    12*t = 8

    t = 8/12 = 2/3

    And it's verified.
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