Boats and Streams Quiz Set 005

Let the speed of the steamer in still water be u and the speed of the river be v. The three speeds are u - v, u and u + v. They are in an A.P. with a common difference equal to v. Since v is also the speed of the river, the required answer is: $1{1/6}$.

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.

The downstream speed = $200/20$ = 10 km/h, and the upstream speed = $200/50$ = 4 km/h. By the shortcut method, the speed of the steamer boat in still water is average of its downstream and upstream speeds. So the required speed = ${10 + 4}/2$ = 7 km/h.

The effective speed of the boat in the stream is 16 - 6 = 10 km/h. The distance is speed × time = 10 × 7 = 70 km.

If v is the speed of the stream, 12 - v = 8, so the speed of the stream is 12 - 8 = 4 km/h. So his downstream speed would be 12 + 4 = 16 km/h.