a boat traveled 160 miles downstream and back. the trip downstream took 8 hours. the trip back took 40 hours. find the speed of the boat in

Question

a boat traveled 160 miles downstream and back. the trip downstream took 8 hours. the trip back took 40 hours. find the speed of the boat in still water and the speed if the current

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    2021-10-11T03:26:23+00:00

    Let speed of the boat in still water = x miles per hour

    Let speed of the current = y miles per hour

    When water and current both flow in same direction then effective speed will be sum of both speeds that is (x+y)

    now plug the given values in formula speed=distance/time

    we get equation:

    (x+y)=160/8

    or x+y=20…(i)

    When water and current both flow in opposite direction then effective speed will be difference of both speeds that is (x-y)

    now plug the given values in formula speed=distance/time

    we get equation:

    (x-y)=160/40

    or x-y=4

    or x=4+y…(ii)

    plug value of x into (i)

    4+y+y=20

    4+2y=20

    2y=16

    y=8

    plug value of y into (ii)

    x=4+8=12

    Hence final answer is given by:

    Speed of the boat in still water = 12 miles per hour

    Speed of the current = 8 miles per hour

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