A motor boat moves slower against the current than in still water, but faster with the current.

A motor boat moves slower against the current than in still water, but faster with the current. Where will it take less time to walk the same distance back and forth – in a river or in a lake? Consider that the operating mode of a motor boat engine is the same everywhere.

Let the speed of the river flow be Vt, and the own speed of a motor boat or the speed in still water will be Vl. Then, against the current, the motor boat moves more slowly at a speed Vpr t = Vl – Vt, but downstream – faster at a speed Vpo t = Vl + Vt. To go the same distance S back and forth in the river, it will take time: tр = S: (Vl – Vt) + S: (Vl – Vt); tr = (2 ∙ S ∙ Vl): (V ^ 2l – V ^ 2t). To go the same distance back and forth in the lake, it will take time: toz = S: Vl + S: Vl; toz = 2 ∙ S ∙ Vl. Let us estimate the difference of these time intervals: tр – toz = (2 ∙ S ∙ Vl): (V ^ 2l – V ^ 2t) – 2 ∙ S ∙ Vl; tr – toz = (2 ∙ S ∙ V ^ 2t): (V ^ 2l – V ^ 2t). Obviously, tp – tp> 0, which means tp> tp.
Answer: In a lake, a motorboat will take less time to travel the same distance back and forth.