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11 July, 11:40

A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours, it can go 40 km upstream and 55 km down-stream. Determine the speed of the stream and that of the boat in still water.

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  1. 11 July, 15:15
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    Average speed of boat = 3.67 km/h

    Average speed of stream = 0.63 km/h

    Step-by-step explanation:

    30 km upstream in 10 hours gives a speed of 30/10 = 3 km/h relative speed of boat and stream

    Same way, 44 km in 10 hrs = 4.4 km/h relative speed of boat and stream.

    Let the speed of the stream be y

    Let the speed of both be x, then

    x - y = 3 ... (1)

    x + y = 4.4 ... (2)

    Subtract 1 from 2

    2y = 1.4

    y = 1.4/2 = 0.7 km/h

    substitute value of y in 1

    x - 0.7 = 3

    x = 3.7 km/h

    Also, 40 km upstream in 13 hrs gives speed of 3.08 km/h

    55 km in 13 hrs gives 4.2 km/h

    Let speed of boat be x and that of stream be y

    x - y = 3.08 ... (1)

    x + y = 4.2 ... (2)

    Subtract 1 from 2

    2y = 1. 12

    y = 0.56 km/h

    Substitute value of y in 1

    x - 0.56 = 3.08

    x = 3.64 km/h

    Average speed of boat = (3.7 + 3.64) / 2

    = 3.67 km/h.

    Average speed of stream = (0.7 + 0.56) / 2 = 0.63 km/h
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