Discussion of Question with ID = 038 under Boats-and-Streams

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Question

The difference of the squares of the downstream and upstream speeds of a boat in a stream is 8. What is the product of the speed of the stream and that of the boat in still water?

A

2.

B

3.

C

4.

D

5.

Soln.
Ans: a

Let the speed of the boat in still water be u, and let v be the speed of the stream. The difference of squares of the speeds is $(u + v)^2 - (u - v)^2$, which is $u^2 + v^2 + 2uv - (u^2 + v^2 - 2uv)$ = 4uv = 8. We get uv = $8/4$ = 2.


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