One fifth of the way in time, the body moved at a speed of 180 km / h. The remaining is 15 km / h.

One fifth of the way in time, the body moved at a speed of 180 km / h. The remaining is 15 km / h. How do I find the average speed?

Given:

v1 = 180 km / h – the speed of the body at one-fifth of the total distance traveled;

v2 = 15 km / h – the speed of the body on the remaining path.

It is required to determine v (km / h) – the average speed of movement along the entire path.

Let the entire path traversed by the body be equal to S.

Then the body passed the first section of the path for:

t1 = (S / 5) / v1 = S / (5 * v1).

The body passed the second part of the path for:

t2 = (4 * S / 5) / v2 = 4 * S / (5 * v2).

The total time is:

t = t1 + t2 = S / (5 * v1) + 4 * S / (5 * v2) = S * (v2 + 4 * v1) / (5 * v1 * v2).

Then the average speed will be equal to:

v = S / t = S / (S * (v2 + 4 * v1) / (5 * v1 * v2)) = 5 * v1 * v2 / (v2 + 4 * v1) =

= 5 * 180 * 15 / (15 + 4 * 180) = 13500/735 = 18.4 km / h.

Answer: The average body speed is 18.4 km / h.