The bus covered one third of the way in a quarter of the time. He covered the rest of the way at a speed of 40 km / h.

The bus covered one third of the way in a quarter of the time. He covered the rest of the way at a speed of 40 km / h. What is the average speed along the entire path?

Let us express the average speed in terms of
vc = (s1 + s2) / (t1 + t2)
then by condition s1 = s / 3 s2 = 2 * s / 3
t2 = 2 * s / (3 * v2) = 3 * t / 4
t = 8 * s / (9 * v2)
t1 = t / 4 = 2 * s / (9 * v2)
vc = (s / 3 + 2 * s / 3) / (2 * s / (9 * v2) + 2 * s / (3 * v2)) = 9 * v2 / 8 = 9 * 40/8 = 45 km / h
Answer: 45 km / h