The train traveled for the first half of the journey at a speed of n = 1.5 times greater than the second half of the journey.

The train traveled for the first half of the journey at a speed of n = 1.5 times greater than the second half of the journey. The average train speed along the entire route is 43.2 km / h. What is the speed of the train on the first and second half of the tracks.

Given:

v1 = 1.5 * v – train speed on the first half of the track;

v2 = v – train speed on the second half of the track;

vav = 43.2 km / h – average train speed.

It is required to determine v1 and v2 (km / h) – the speed of the train on the first and second half of the track.

Let S be the entire distance traveled by the train, and t be the time it took for the train to cover this distance. Then:

vav = S / t = S / (S / v1 + S / v2) = S / (S / (2 * 1.5 * v) + S / (2 * v)) =

= S / (S / (3 * v) + S / (2 * v)) = S / ((2 * S + 3 * S) / (6 * v)) = S / ((5 * S) / (6 * v)) = 6 * v / 5, hence:

v = 5 * vav / 6 = 5 * 43.2 / 6 = 172.8 / 3 = 36 km / h.

v2 = v = 36 km / h.

v1 = 1.5 * v = 1.5 * 36 = 54 km / h.

Answer: on the first half of the journey, the train speed was 54 km / h, on the second half of the journey – 36 km / h.