The car drove the first third of the way at an average speed of 15 m / s. And he covered the rest of the way

The car drove the first third of the way at an average speed of 15 m / s. And he covered the rest of the way at a speed of 20 m / s. What is the average vehicle speed (m / s) over the entire route?

S1 = S / 3.

V1 = 15 m / s.

V2 = 20 m / s.

Vav -?

To find the average speed Vav of the car, it is necessary to divide the entire S traversed by it by the time of its movement t: Vav = S / t.

The time of movement of the car during the passage of the entire path is expressed by the sum: t = t1 + t2, where t1 is the time of movement on the first part of the path, t2 is the time of movement on the second part of the path.

Since the car moved uniformly in the first and second sections, we will express the time of their movement in each section by the formulas:

t1 = S1 / V1 = S / 3 * V1.

t2 = S2 / V2.

Since S1 = S / 3, then S2 = S – S1 = S – S / 3 = 2 * S / 3.

t2 = 2 * S / 3 * V2.

t = S / 3 * V1 + 2 * S / 3 * V2 = (S * V2 + 2 * S * V1) / 3 * V1 * V2 = (S * V2 + 2 * S * V1) / 3 * V1 * V2 = S * (V2 + 2 * V1) / 3 * V1 * V2.

Vav = S * 3 * V1 * V2 / S * (V2 + 2 * V1) = 3 * V1 * V2 / (V2 + 2 * V1).

Vav = 3 * 15 m / s * 20 m / s / (20 m / s + 2 * 15 m / s) = 18 m / s.

Answer: the car was moving at an average speed Vav = 18 m / s.