# The boat sailed at a speed of 36 km / h. in the opposite direction

The boat sailed at a speed of 36 km / h. in the opposite direction, he swam at a speed of 8.0 m / s. Determine the average speed of the boat along the entire route.

V1 = 36 km / h = 10 m / s.

V2 = 8 m / s.

S1 = S2.

Vav -?

To find the average speed of movement Vav, it is necessary to divide the entire distance traveled by the boat S by the time of its movement t along the entire path: Vav = S / t.

The travel time of the entire path is expressed by the sum: t = t1 + t2, where t1 is the time of movement on the first half of the path, t2 is the time of movement on the second half of the path.

t1 = S1 / V1.

t2 = S2 / V2 = S1 / V2.

t = S1 / V1 + S1 / V2 = (S1 * V2 + S1 * V1) / V1 * V2 = S1 * (V2 + V1) / V1 * V2.

S = S1 + S2 = 2 * S1.

Vav = 2 * S1 * V1 * V2 / S1 * (V2 + V1) = 2 * V1 * V2 / (V2 + V1).

Vav = 2 * 10 m / s * 8 m / s / (8 m / s + 10 m / s) = 8.9 m / s.

Answer: the average speed of the boat was Vav = 8.9 m / s.

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