Boats and Streams Quiz Set 018

The downstream speed = $70/7$ = 10 km/h, and the upstream speed = $24/6$ = 4 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 = ${10 - 4}/2$ = 3 km/h.

If the distance travelled is D and the speed of the current is R km/h, we have $D/{12/7 - R}$ = 3 × $D/{12/7 + R}$. Cancelling D, and solving for R, we get R = ${6/7}$ km/h. So downstream speed would be ${6/7}$ + $12/7$ = $2{4/7}$ km/h.

The downstream speed is the speed along the direction of the flow of the stream. It is equal to the sum of the speed of the boat in still water and the speed of the stream. So the speed downstream is 7 + 2 = 9 km/h.

Let the speed of the boat in still water be u, and let v be the speed of the stream. The product of the upstream and downstream speeds of the boat is $(u + v) × (u - v)$, which is $u^2 - v^2$, and, therefore, the required answer = 12.

The downstream speed = $28/2$ = 14 km/h, and the upstream speed = $56/4$ = 14 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 = ${14 - 14}/2$ = 0 km/h.