Boats and Streams Quiz Set 008

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 8 + 6 = 14 km/h.

If v is the speed of the stream, 14 - v = 8, so the speed of the stream is 14 - 8 = 6 km/h. So his downstream speed would be 14 + 6 = 20 km/h.

The effective speed of the boat in the stream is 16 - 8 = 8 km/h. The distance is speed × time = 8 × 7 = 56 km.

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 $L/{u - v} = 8 × L/{u + v}$. We can solve this equation for u/v to get u/v = ${8 + 1}/{8 - 1}$ = $1{2/7}$.

By the shortcut method, the speed of the boat in still water is average of downstream and upstream speeds. So the required speed = ${16 + 12}/2$ = 14 km/h.