in still water a boat averages 18 miles per hour. it takes the same amount of time to travel 4 miles downstream, with the current, as it doe

Question

in still water a boat averages 18 miles per hour. it takes the same amount of time to travel 4 miles downstream, with the current, as it does 2 miles upstream, against the current, what is the rate of the water current

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Caroline 4 weeks 2021-09-24T04:32:36+00:00 1 Answer 0

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    2021-09-24T04:33:42+00:00

    Answer:

    The rate of water current = 6 mi / h

    Step-by-step explanation:

    Speed of the boat in still water = u = 18 mi / h

    Let Speed of the current = v

    Now downstream speed is given by = u + v

    And upstream speed is given by = u – v

    Now time taken to travel 4 miles in downstream =  \frac{4}{u + v}  ———————-(1)

    And time taken to travel 2 miles in upstream =  \frac{2}{u - v} —————————-(2)

    Now from the question equation (1) = equation (2)

    \frac{4}{u + v} = \frac{2}{u - v}

    ⇒ 4 u – 4 v = 2 u + 2 v

    ⇒ 2 u = 6 v

    ⇒ u = 3 v

    ⇒ given that u = 18 mi / h

    ⇒ v = \frac{18}{3}

    ⇒ v = 6 mi / h

    Thus the rate of water current = 6 mi / h

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