A quarter of the entire time of movement, the speed was 20 km / h, and the rest of the time was

A quarter of the entire time of movement, the speed was 20 km / h, and the rest of the time was 30 km / h. Find the average speed of movement.

v1 = 20 km / h – body speed for the 4th part of the entire movement time;

v2 = 30 km / h – body speed for the remaining time of movement.

It is required to determine the average speed vav (km / h).

Let the body have traveled a full path in time t.

Then, in time 1/4 t, it passed the path:

S1 = v1 * t / 4.

And in the remaining time it has passed the way:

S2 = v2 * 3 * t / 4.

Full path that the body has traveled:

S = S1 + S2 = v1 * t / 4 + 3 * v2 * t / 4 = t * (v1 + 3 * v2) / 4.

Then the average speed of the body is:

vav = S / t = t * (v1 + 3 * v2) / 4 * t = (v1 + 3 * v2) / 4 = (20 + 3 * 30) / 4 = (20 + 90) / 4 =

= 110/4 = 27.5 km / h.

Answer: the average body speed is 27.5 km / h.