Boats and Streams Quiz Set 019

The downstream speed = $84/6$ = 14 km/h, and the upstream speed = $40/4$ = 10 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 = ${14 - 10}/2$ = 2 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 = 20.

Speed of the boat in still water is the difference between its downstream speed and the speed of the stream, which is 16 - 4 = 12 km/h. Hence, the speed of the boat against the current is 12 - 4 = 8 km/h.

Let the distance be L and the speed of the boat in still water be u, with v being the speed of the stream. We are given $L/{u - v} = 6 × L/{u + v}$. We can solve this equation for u/v to get u/v = ${6 + 1}/{6 - 1}$ = $1{2/5}$.

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: ${5/8}$.