Q. A motor boat whose speed is 24 km/hr in still water takes 1 hr more to go 32km upstream than to return downstream to the same spot. Find the speed of the stream.
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Upstream
24 + y = 32/t
Downstream
24 - y = 32/(t+1)
Add both the equation
48 = 32(1/t + 1/(t+1))
48/32 = (t+1+t)/t(t+1)
3/2 * t(t+1) = (2t+1)
3/2t^2 + 3/2*t = 2t + 1
3/2t^2 - 1/2*t - 1 = 0
On solving the quadratic equation,
t = 1
So, speed of the stream -
24 + y = 32/t
y = 32-24 = 8 km/hr
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