The average speed of a cyclist along the entire path is 40 km / h. The first half of the journey

The average speed of a cyclist along the entire path is 40 km / h. The first half of the journey he drove at a speed of 60 km / h. How fast did the cyclist go the rest of the way?

Initial data: Vav. (average speed of a cyclist along the entire path) = 40 km / h, V1 (speed of a cyclist in the first half of the journey) = 60 km / h; S1 = S2 = 0.5S.

Formula for calculating the average speed of a cyclist:

Vav. = (S1 + S2) / (t1 + t2) = (S1 + S2) / (S1 / V1 + S2 / V2) = S / (0.5S / 60 + 0.5S / V2) = 1 / (1 / 120 + 1 / 2V2).

1/40 = 1/120 + 1 / 2V2.

1 / 2V2 = 1/40 – 1/120 = 2/120 = 1/60.

2V2 = 60.

V2 = 60/2 = 30 km / h.

Answer: The cyclist traveled the rest of the way at a speed of 30 km / h.