Boats and Streams Quiz Set 010

The downstream speed = $392/28$ = 14 km/h, and the upstream speed = $392/98$ = 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 = ${14 - 4}/2$ = 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 = ${8 + 6}/2$ = 7 km/h.

The effective speed of the boat in the stream is 12 - 4 = 8 km/h. The distance is speed × time = 8 × 6 = 48 km.

The effective speed of the aircraft in the air is 14 + 4 = 18 km/h. The distance is speed × time = 18 × 3 = 54 km.

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 = 8.