Boats and Streams Quiz Set 020

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.

By the shortcut method, the speed of the boat in still water is average of downstream and upstream speeds. So the required speed = ${12 + 12}/2$ = 12 km/h.

The effective speed of the aircraft in the air is 10 + 4 = 14 km/h. The distance is speed × time = 14 × 4 = 56 km.

Let the speed of the boat in still water be u and the speed of the stream 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, and u as its middle term. Since u is also the speed of the boat in still water, the required answer is: 1.

The downstream speed = $512/32$ = 16 km/h, and the upstream speed = $512/64$ = 8 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 = ${16 - 8}/2$ = 4 km/h.