The electric train had to travel 840 km. Being 20 minutes late half way, I increased my speed by 6 km / h in order

The electric train had to travel 840 km. Being 20 minutes late half way, I increased my speed by 6 km / h in order to arrive on time. how long did the electric train take to complete the entire journey?

We denote by v the speed of the electric train on the first section of the track.

According to the condition of the problem, the entire distance that the train had to travel is 840 km, therefore, the first half of the journey is 840/2 = 420 km and the time spent by the train to pass this section is 420 / v.

According to the condition of the problem, the train passed the second half of the journey at a speed of 6 km / h more than the first, therefore, the time spent by the train to pass the second section is 420 / (v + 6).

It is known that on the first half of the journey the train was late by 20 minutes, which is 1/3 hour, and in the second half it eliminated the lag, therefore, we can draw up the following equation:

420 / v = 420 / (v + 6) + 1/3.

We solve the resulting equation:

420 / v – 420 / (v + 6) = 1/3;

420 * (1 / v – 1 / (v + 6)) = 1/3;

420 * (6 / (v * (v + 6))) = 1/3;

420 * 6 = (1/3) * v * (v + 6);

2520 = (d / 3) * (v ^ 2 + 6v);

v ^ 2 + 6v = 2520 / (1/3);

v ^ 2 + 6v = 7560;

v ^ 2 + 6v – 7560 = 0;

v = -3 ± √ (9 + 7560) = -3 ± 87;

v = -3 + 87 = 84 km / h.

Consequently, the train spent 420 / v + 420 / (v + 6) = 420/84 + 420 / (84 + 6) = 5 + 14/3 = 9 2/3 h = 9 h 40 min for the whole journey.

Answer: the train spent 9 hours and 40 minutes on the whole journey.