Boats and Streams Quiz Set 007

Let v km/h be the rate of flow of the stream. Upstream and downstream times are equal. So $2/{28 - v}$ = $12/{28 + v}$. Solving for v, or verifying by putting the given options one by one, we get v = 20 km/h.

The downstream speed = $1152/72$ = 16 km/h, and the upstream speed = $1152/96$ = 12 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 = ${16 + 12}/2$ = 14 km/h.

If v is the speed of the stream, 12 - v = 6, so the speed of the stream is 12 - 6 = 6 km/h. So his downstream speed would be 12 + 6 = 18 km/h.

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.

The downstream speed = $64/8$ = 8 km/h, and the upstream speed = $64/16$ = 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 = ${8 + 4}/2$ = 6 km/h.