Q. 364.1( 16 Votes )
A boat goes 12 km upstream and 40 km downstream in 8 hours. It can go 16 km upstream and 32 km downstream in the same time. Find the speed of the boat in still water and the speed of the stream.
Answer :
Let the speed of the boat in still water and the speed of the stream be v kmph and u kmph respectively.
Speed of the boat in upstream direction = v - u
Speed of the boat in downstream direction = v + u
According to question -
12/(v - u) + 40/(v + u) = 8
⇒12x + 40y = 8 [ Let 1/(v - u) = x and 1/(v + u) = y ]
⇒3x + 10y = 2 .....(1)
and,
16/(v - u) + 32/(v + u) = 8
⇒16x + 32y = 8 [Let 1/(v - u) = x and 1/(v + u) = y]
⇒ 2x + 4y = 1.....(2)
From equation (1), we get -
x = (2 - 10y)/3.....(3)
Substituting the value of x in equation (2), we get -
⇒ 4 - 8y = 3
⇒ 8y = 1
∴ y = 1/8
⇒ v + u = 8.....(4)
substituting the value of y in equation (3), we get -
x = 1/4
⇒ v - u = 4.....(5)
Adding equations (4) and (5), we get -
v = 6
Substituting the value of v in equation (4), we get -
u = 2
Thus, Speed of the boat in still water = 6 kmph and speed of stream = 2 kmph.
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KC Sinha - Mathematics