Boats need to sail 240 meters back and forth, once on the river and another time on the lake.

Boats need to sail 240 meters back and forth, once on the river and another time on the lake. The speed of the river is 1 meter per second, and the speed of the boat relative to the water is 5 meters per second. How much longer will it take a boat to move along the river than along the lake?

S1 = 240 m.

Vt = 1 m / s.

Vl = 5 m / s.

tр – to -?

Since the water does not move in the lake, the time of movement of the boat back and forth across the lake tо is found by the formula: tо = 2 * S1 / Vл.

tо = 2 * 240 m / 5 m / s = 96 s.

The time of movement by boat on the river tp is expressed by the formula: tp = S1 / (Vl + Vt) + S1 / (Vl – Vt).

tr = 240 m / (5 m / s + 1 m / s) + 240 m / (5 m / s – 1 m / s) = 40 s + 60 s = 100 s.

tр – tо = 100 s – 96 s = 4 s.

Answer: the boat’s movement back and forth along the river will last 4 s longer than along the lake: tp – to = 4 s.