Q3) A boat takes 9 hours to travel 30 km upstream and 40 km downstream but it takes 12 hours to travel 42 km upstream and 50 km downstream.

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Q3) A boat takes 9 hours to travel 30 km upstream and 40 km downstream but it takes 12 hours to travel 42 km upstream and 50 km downstream. Find the speed of the boat in still water and the speed of the stream

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Eloise 2 weeks 2021-11-19T16:31:21+00:00 2 Answers 0 views 0

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    2021-11-19T16:32:33+00:00

    Answer:

    SEE THE ATTACHMENT FOR DETAILED SOLUTION TO THE QUESTION DUDE ❗️❗️

    0
    2021-11-19T16:33:17+00:00

    SOLUTION ::

    Let the speed of the boat in still water = x km/h

    The speed of the stream = y km/h

    We know that

    Total time = Upstream distance/upstream speed + Downstream dist/downstream speed

    Upstream speed

    = speed of boat – speed of stream

    = x – y

    Down stream speed = x + y

    BY THE GIVEN CONDITION

    30/x-y + 40/x+y = 9 …………. (i)

    42/x-y + 50/x+y = 12 ………….(ii)

    Multiplying eq.(i) by 5 & eq.(ii) by 4

    150/x-y + 200/x+y = 45 ……(iii)

    168/x-y + 200/x+y = 48 ……(iv)

    Now (iii) – (iv) gives

    -18/x-y = – 3

    x-y = 6 …..(v)

    Substituting (v) in (iii)

    150/x-y + 200/x+y = 45

    150/6 + 200/x+y = 45

    200/x+y = 20

    x + y = 10……..(vi)

    Adding (v) & (vi) We get

    2x = 16

    x = 8

    8+y = 10

    y= 2

    Hence speed of boat = 8 km/h

    Speed of stream = 2 km/h

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