Will it take the same amount of time to travel the same distance S by boat back and forth on the river and on the lake?

Will it take the same amount of time to travel the same distance S by boat back and forth on the river and on the lake? River speed V1, speed of the boat relative to water V2.

Given:

S is the distance between the river and the boat;

V1 is the speed of the river flow;

V2 is the speed of the boat relative to the water.

It is required to determine whether the boat will take the same time to travel the distance S there and back.

Let the boat move along the river for the first time. Then its speed relative to the ground will be equal to:

V = V1 + V2.

The time will be equal to:

t1 = S / V = ​​S / (V1 + V2).

When the boat goes back (against the stream of the river), its speed relative to the ground will be equal to:

V = V2 – V1.

The time will be equal to:

t2 = S / V = ​​S / (V2 – V1).

Since t1 is not equal to t2 (S / (V1 + V2) is not equal to S / (V2 – V1)), the time will not be the same.

Answer: the time it takes for a boat to travel there and back will not be the same.