Question

- A boat covers 32 km upstream and 36 km downstream in 7 hours. Also, it covers 40 km
upstream and 48 km downstream in the same time. Find the speed of the boat in still water and
that of the stream.
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Answer 1

Let the speed of the boat in still water is x kms/hr and the speed of the stream

is y kms/hr , thus speed of boat upstream = (x-y) kms/hr. and speed of boat

downstream =(x+y) kms/hr. , acordingly:-

32/(x-y) +36/(x+y) = 7…………..(1)

40/(x-y)+48/(x+y) = 9……………(2)

{1/(x-y)}/(324–336)={1/x+y}/(280–288) = -1/(32×48–36×40)

1/{-12.(x-y)} = 1/{-8.(x+y)}= -1/{8×12.(16–15)}

1/{3.(x-y) }= 1/{2.(x+y)}= 1/24.

Thus , x-y = 8………….(3)

x+y= 12………………….(4)

Adding eqn (3) and (4)

2x= 20 => x=20/2=10 kms/hr. ,putting x=10. in. eqn. (4 )

10 + y = 12 => y = 12–10=2 kms/hr.

Speed of the boat in still water = 10kms/hr. and speed of the stream = 2kms/hr.

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