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### Question

The difference of the squares of the downstream and upstream speeds of a boat in a stream is 12. What is the product of the speed of the stream and that of the boat in still water?

**A**

3.

**B**

4.

**C**

2.

**D**

6.

**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 = 12. We get uv = $12/4$ = 3.