Boats and Streams Quiz Set 001

Let the speed of the boat in still water be u and the speed of the stream 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, and u as its middle term. Since u is also the speed of the boat in still water, the required answer is: $1{1/5}$.

The downstream speed = $288/24$ = 12 km/h, and the upstream speed = $288/72$ = 4 km/h. By the shortcut method, the speed of the boat in still water is average of the downstream and upstream speeds of the boat. So the required speed = ${12 + 4}/2$ = 8 km/h.

The effective speed of the aircraft in the air is 12 + 8 = 20 km/h. The distance is speed × time = 20 × 8 = 160 km.

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 the distance be L and the speed of the boat in still water be u, with v being the speed of the stream. We are given $L/{u - v} = 8 × L/{u + v}$. We can solve this equation for u/v to get u/v = ${8 + 1}/{8 - 1}$ = $1{2/7}$.