Boats and Streams Quiz Set 017

If the distance travelled is D and the speed of the current is R km/h, we have $D/{12/5 - R}$ = 3 × $D/{12/5 + R}$. Cancelling D, and solving for R, we get R = ${6/5}$ km/h. So downstream speed would be ${6/5}$ + $12/5$ = $3{3/5}$ km/h.

By the shortcut method, the speed of the boat in still water is average of downstream and upstream speeds. So the required speed = ${14 + 8}/2$ = 11 km/h.

The downstream speed = $280/20$ = 14 km/h, and the upstream speed = $280/70$ = 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 = ${14 + 4}/2$ = 9 km/h.

By the shortcut method, the speed of the stream is half of the difference between the downstream and upstream speeds of the boat. So the required speed = ${14 - 4}/2$ = 5 km/h.

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 = ${8 + 1}/{8 - 1}$ = $1{2/7}$.