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Tuesday, September 16, 2008

Q) A motorboat going downstream came across a bottle floating in the river at a point A . After 60 minutes of further motion, it turned back and after some time passed the bottle at a distance 6 km from point A. Find the flow speed of the river (in km/hr) assuming the duty of engine to be constant?


A) Let Vf = velocity of flow & V = velocity of boat

Distance covered by boat in 60 mins = (V + Vf) x 1 hour = V + Vf

Also
6 km = Vf * (60 min + T) where T is time taken for the boat to return to the bottle again.
6 = Vf [1 hour + (V + Vf - 6) / (V - Vf) ] ........... V - Vf is net speed for upstream motion
6 = Vf (2V - 6) / V - Vf
6V - 6Vf = 2V.Vf - 6Vf
6V = 2V.Vf
Vf = 3

So the flow speed = 3 km/hr


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