The car traveled three quarters of the way at a speed of 20m / s, and the rest of the way at a speed of 10m / s.

The car traveled three quarters of the way at a speed of 20m / s, and the rest of the way at a speed of 10m / s. What is the average speed all the way?

Given:

v1 = 20 m / s – vehicle speed at 3/4 of the distance traveled;

v2 = 10 m / s – the speed of the car in a section of 1/4 of the distance traveled.

It is required to determine Vav (m / s) – the average speed of the vehicle along the entire path.

Let S be the entire path traveled by the car.

Let’s find the time it took for the car to go all the way:

The first section of the path is t1 = 3 * S / (4 * v1). Second section of the path: t2 = S / (4 * v2).

Full time:

t = t1 + t2 = 3 * S / (4 * v1) + S / (4 * v2) = (3 * S * v2 + S * v1) / (4 * v1 * v2) =

= S * (3 * v2 + v1) / (4 * v1 * v2).

Then the average speed will be equal to:

Vav = S / t = S / (S * (3 * v2 + v1) / (4 * v1 * v2)) = S * (4 * v2 * v1) / S * (3 * v2 + v1) =

4 * v1 * v2 / (3 * v2 + v1) = 4 * 20 * 10 / (3 * 10 + 20) = 800 / (30 + 20) = 800/50 = 16 m / s.

Answer: the average speed is 16 m / s.