The car traveled 1/4 of the way at a speed of 108 km / h, and the rest of the way at a speed

The car traveled 1/4 of the way at a speed of 108 km / h, and the rest of the way at a speed of 72 km / h. Find the average vehicle speed.

Let’s take the entire path that the car has traveled for X.

Then the length of the path (x1) that the car traveled at a speed of 108 km / h is:

x1 = t1 * 108, where t1 is the time it took for the car to cover this distance (in hours).
x1 = 0.25 * X;

0.25 * X = t1 * 108;

t1 = 0.25 * X / 108.

The length of the path (x2) that the car traveled at a speed of 72 km / h is:

x2 = t2 * 72, where t2 is the time it took for the car to cover this distance (in hours).
x2 = 0.75 * X;

0.75 * X = t2 * 72;

t2 = 0.75 * X / 72.

The average speed is determined as the quotient of dividing the entire path X by the entire time (t1 + t2):

Vav = X / (t1 + t2);

Vav = X / (0.25 * X / 108 + 0.75 * X / 72);

Vav = X / (0.25 * 2 * X / 216 + 0.75 * 3 * X / 216);

Vav = X * 216 / (0.5 * X + 2.25 * X);

Vav = 216 / (0.5 + 2.25);

Vav = 216 / 2.75;

Vav = 96 km / h.

Answer: the average speed of the car for the entire journey was 96 km / h.