Boats and Streams Quiz Set 009

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 = 28. We get uv = $28/4$ = 7.

Let v km/h be the rate of flow of the stream. Upstream and downstream times are equal. So $11/{56 - v}$ = $17/{56 + v}$. Solving for v, or verifying by putting the given options one by one, we get v = 12 km/h.

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.

If v is the speed of the stream, 14 - v = 4, so the speed of the stream is 14 - 4 = 10 km/h. So his downstream speed would be 14 + 10 = 24 km/h.

The effective speed of the aircraft in the air is 14 + 8 = 22 km/h. The distance is speed × time = 22 × 7 = 154 km.