The cyclist traveled the first third of the path at a speed of 10 m / s, then half of the path

The cyclist traveled the first third of the path at a speed of 10 m / s, then half of the path at a speed of 6 m / s and the rest of the path at a speed of 2 m / s. What is the average speed of a cyclist?

Data: S1 (first part of the path) = 1/3 S; V1 (speed on the first part) = 10 m / s; S2 (second part of the path) = 1/2 S; V2 (speed on the second part) = 6 m / s; V3 (speed on the rest of the path) = 2 m / s.

Average speed of the taken cyclist: V = S / (t1 + t2 + t3) = S / (S1 / V1 + S2 / V2 + S3 / V3) = S / (S1 / V1 + S2 / V2 + (S – S1 – S2 ) / V3) = S / (S / 3V1 + S / 2V2 + S / 6V3) = 1 / (1 / 3V1 + 1 / 2V2 + 1 / 6V3).

Calculation: V = 1 / (1 / (3 * 10) + 1 / (2 * 6) + 1 / (6 * 2)) = 1 / 0.2 = 5 m / s.