A boat travels upstream for 360 miles in 4 hours and returns in 3 hours traveling downstream in a local stream of water. What is the rate of

Question

A boat travels upstream for 360 miles in 4 hours and returns in 3 hours traveling downstream in a local stream of water. What is the rate of the boat in still water and the rate of the current?

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Khánh Gia 3 weeks 2021-08-23T23:36:54+00:00 1 Answers 2 views 0

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    2021-08-23T23:37:55+00:00

    Answer:

    Rate of boat in still water = 105 mph

    Rate of current = 15 mph

    Explanation:

    Let the speed of the boat in still water be v_b.

    Let the speed of the current be v_c.

    When the boat goes upstream, it moves against the current. Hence, its velocity will be relative to that of the current. This is given by 360/4 = 90 mph.

    This relative velocity is the difference between the speed of the boat in still water and that of the current:

    v_b - v_c = 90

    In the downstream, the boat moves with the current. The resultant velocity is the sum of the velocities of boat in still water and current.

    v_b+v_c = 360/3 =120

    Solving both equations simultaneously by elimination method,

    2v_b = 210                             (adding both equations)

    v_b = 105\text{ mph}

    2v_c = 30                               (subtracting the first from the second equation)

    v_c =15\text{ mph}

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