Boats and Streams Quiz Set 002

Let v km/h be the rate of flow of the stream. Upstream and downstream times are equal. So $9/{84 - v}$ = $19/{84 + v}$. Solving for v, or verifying by putting the given options one by one, we get v = 30 km/h.

The boats are same, so they have the same speed in still water. Let the upstream speed be u and v be the downstream speed, and let the initial distance between them be L. When they meet they have travelled for the same time. So $(L/8)/u = ({7L}/8)/v$. The ratio $v/u$ = 7.

The effective speed of the boat in the stream is 10 - 4 = 6 km/h. The distance is speed × time = 6 × 5 = 30 km.

The boats are same, so they have the same speed in still water. Let the upstream speed be u and v be the downstream speed, and let the initial distance between them be L. When they meet they have travelled for the same time. So $(L/5)/u = ({4L}/5)/v$. The ratio $v/u$ = 4.

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: $1{1/2}$.