The pedestrian passed one third of its path at a speed of 4 m / s, and the rest – at a speed of 3 m / s.

The pedestrian passed one third of its path at a speed of 4 m / s, and the rest – at a speed of 3 m / s. Determine the average speed of movement.

Given:

v1 = 4 m / s – pedestrian speed on one third of the way;

v2 = 3 m / s – the speed of the pedestrian on the remaining path.

It is required to find the average passenger speed vav (m / s).

The entire path traveled by a pedestrian is S.

Then the time during which the pedestrian covered the first leg of the path is equal to:

t1 = S / (3 * v1).

The time during which the pedestrian covered the remaining path is equal to:

t2 = 2 * S / (3 * v2).

The total travel time of a pedestrian is:

t = t1 + t2 = S / (3 * v1) + 2 * S / (3 * v2) = S * (v2 + 2 * v1) / (3 * v1 * v2)

The average speed of a pedestrian is:

vср = S / t = S / (S * (v2 + 2 * v1) / (3 * v1 * v2)) = 3 * v1 * v2 / (v2 + 2 * v1) =

= 3 * 4 * 3 / (3 + 2 * 4) = 36/11 = 3.3 m / s.

Answer: the average speed of a pedestrian is 3.3 m / s.