It took a crew 9 h 36 min to row 8 km upstream and back again. If the rate of flow of the stream was 2 km/h, what was the rowing speed of th

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It took a crew 9 h 36 min to row 8 km upstream and back again. If the rate of flow of the stream was 2 km/h, what was the rowing speed of the crew in still water?

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Thành Công 2 weeks 2021-08-29T03:22:18+00:00 1 Answers 0 views 0

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    2021-08-29T03:24:17+00:00

    Answer:

    3 km/h

    Explanation:

    Let’s call the rowing speed in still water x, in km/h.

    Rowing speed in upstream is: x – 2 km/h

    Rowing speed in downstream is: x + 2 km/h

    It took a crew 9 h 36 min ( = 9 3/5 = 48/5) to row 8 km upstream and back again. Therefore:

    8/(x – 2) + 8/(x + 2) = 48/5      (notice that: time = distance/speed)

    Multiplying by x² – 2², which is equivalent to (x-2)*(x+2)

    8*(x+2) + 8*(x-2) =  (48/5)*(x² – 4)

    Dividing  by 8

    (x+2) + (x-2) = (6/5)*(x² – 4)

    2*x = (6/5)*x² – 24/5

    0 =  (6/5)*x² – 2*x – 24/5

    Using quadratic formula

    x = \frac{2 \pm \sqrt{(-2)^2 - 4(6/5)(-24/5)}}{2(6/5)}

    x = \frac{2 \pm 5.2}{2.4}

    x_1 = \frac{2 + 5.2}{2.4}

    x_1 = 3

    x_2 = \frac{2 - 5.2}{2.4}

    x_2 = -1\; 1/3

    A negative result has no sense, therefore the rowing speed in still water was 3 km/h

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