The tourist covered the first half of the journey at a speed of 6 km / h. The average speed along the entire route was 10 km / h

The tourist covered the first half of the journey at a speed of 6 km / h. The average speed along the entire route was 10 km / h. What is the tourist’s speed on the second section of the path.

Given:
V1 = 6 km / h
Vav = 10 km / h
V2 =?
Decision:
Vav = S / t
t1 = S / (2 * V1)
t2 = S / (2 * V2)
Vav = S / ((S / (2 * v1)) + (S / (2 * v2)))
Vcr = 1 / ((V2 + V1) / 2 * (V1 * V2))
Vav = 2 * V1 * V2 / (V2 + V1)
Vcr * (V2 + V1) = 2 * V1 * V2
Vcr * V2-2 * V1 * V2 = -Vcr * V1
V2 (Vcr-2 * V1) = – Vcr * V1
V2 = -Vcr * V1 / (Vcr-2 * V1)
V2 = Vcr * V1 / (2 * V1-Vcr)
V2 = 10 * 6 / (2 * 6-10) = 30 km / h
Answer: 30 km / h