Thomas is going downstream on a motorboat and passes a raft at point . Exactly after that, his motorboat turns around to go back upstream. In this return journey, he notices the same raft at a distance of from point .
Find the flow velocity of the stream in assuming the duty of the engine to be constant.
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Assume v B , v R to be the speeds of the boat and the river respectively.
Let the boat covers x distance in 1 hr. with a speed v B + v R since downstream ,therefore x = v B + v R
Now when it returns at the edge of 6 kms before the point A he revisits the raft. Int his upstream the distance he travelled is v B + v R − 6 with a speed v B − v R
So total time consumed, T = 1 + v B − v R v B + v R − 6
Again this is the time in which the raft traversed 6 km with the flow of the river so we must have T = v R 6
1 + v B − v R v B + v R − 6 = v R 6 v B − v R + v B + v R − 6 = v R 6 ( v B − v R ) v R ( 2 v B − 6 ) = 6 ( v B − v R ) v B v R = 3 v B v R = 3