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.
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