The train passed the first quarter of the journey at a speed of 60 km / h. The average speed along the entire

The train passed the first quarter of the journey at a speed of 60 km / h. The average speed along the entire route was 40 km / h. At what speed did the train travel the rest of the journey?

Data: V1 (speed in the first quarter of the way) = 60 km / h; Vav. (average train speed along the entire route) = 40 km / h; S1 (length of the first part of the path) = 0.25S; S2 (remaining path length) = 0.75S.

Average speed: Vav. = S / (t1 + t2) = S / (S1 / V1 + S2 / V2) = S / (0.25S / V1 + 0.75S / V2).

40 = 1 / (0.25 / 60 + 0.75 / V2).

40 * (0.25 / 60 + 0.75 / V2) = 1.

1/6 + 30 / V2 = 1.

30 / V2 = 1 – 1/6 = 5/6.

5 * V2 = 30 * 6.

V2 = 180/5 = 36 km / h.

Answer: The speed for the rest of the way is 36 km / h.