The cyclist traveled half the way at 10 m / s and half the remaining time at 8 m / s, and then traveled to the end of the journey

The cyclist traveled half the way at 10 m / s and half the remaining time at 8 m / s, and then traveled to the end of the journey at 4 m / s. Determine the average speed of the cyclist along the entire path.

Vav. = S / t, where S is the distance traveled (S = S1 + S2 + S3, S1 = 1/2 S, S2 + S3 = 1 / 2S), t is the movement time (t = t1 + t2 + t3, t2 = t3).
Since t2 = t3, then the average speed on the second section of the track: Vav2 = (8 + 4) / 2 = 6 m / s.
S1 = V1 * t1, V1 = 10 m / s.
t1 = S1 / V1 = (1 / 2S) / 10.
Let’s calculate the average speed:
Vav. = S / (t1 + t2 + t3) = S / (1 / 2S / 10 + 1 / 2S / 6) = S / (0.05S + 0.083S) = 1 / 0.133 = 7.52 m / s.
Answer: The average speed of a cyclist is 7.52 m / s.