Up the river, the pleasure boat sailed at a speed of v1 and returned back at a speed of v2.

Up the river, the pleasure boat sailed at a speed of v1 and returned back at a speed of v2. determine the average speed of the boat along the entire walking route.

1. Let’s designate: 2x – the distance that the boat sailed on the walking route.

2. Let’s find the time during which the boat sailed up the river:

x / u1;

3. Let’s find the time for which the boat returned back:

x / u2;

4. Let’s find the total time of movement:

(x / u1) + (x / u2) = (x * u2 + x * u1) / (u1 * u2);

5. Average speed – the ratio of the total distance traveled to the total time. Let’s find it:

2x / ((x * u2 + x * u1) / (u1 * u2)) = 2x * u1 * u2 / (x * (u1 + u2)) = 2u1 * u2 / (u1 + u2);

Answer: the average speed of the boat is given by the expression: 2u1 * u2 / (u1 + u2).