A boat travels between two cities that are 18 miles apart. When going downstream, with the current, the trip takes 9/8 hour(s). Returning up

Question

A boat travels between two cities that are 18 miles apart. When going downstream, with the current, the trip takes 9/8 hour(s). Returning upstream, against the current, the boat covers the same distance in 9/5 hour(s). What is the current of the river? miles per hour What is the speed of the boat in still water?

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Piper 3 weeks 2021-11-06T14:21:08+00:00 1 Answer 0 views 0

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    2021-11-06T14:22:51+00:00

    Answer: the speed of the boat in still water is 13 mph.

    the current of the river is 3 mph

    Step-by-step explanation:

    Let x represent the speed of the boat in still water.

    Let y represent the current of the river.

    The boat travels between two cities that are 18 miles apart.

    When going downstream, with the current, the trip takes 9/8 hour(s). The total speed of the boat would be (x + y) mph

    Distance = speed × time

    Distance travelled while going downstream is

    18 = 9/8(x + y)

    18 = 1.125(x + y)

    Dividing both sides by 1.125, it becomes

    16 = x + y – – – – – – – – – – 1

    Returning upstream, against the current, the boat covers the same distance in 9/5 hour(s). The total speed of the boat would be (x – y) mph. Distance travelled while going upstream is

    18 = 9/5(x – y)

    18 = 1.8(x – y)

    Dividing both sides by 1.8, it becomes

    10 = x – y – – – – – – – – – – 2

    Adding equation 1 to equation 2, it becomes

    26 = 2x

    x = 26/2 = 13

    Substituting x = 13 into equation 2, it becomes

    10 = 13 – y

    y = 13 – 10

    y = 3

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