# The cyclist traveled the first half of the trip at 12 km / h, and the second half of the trip at a different speed.

**The cyclist traveled the first half of the trip at 12 km / h, and the second half of the trip at a different speed. The average speed for the entire trip is 8 km / h. Determine the speed of the cyclist on the second leg.**

To calculate the value of the speed of the indicated cyclist on the second section of the path, we apply the formula: Vav = S / (tn + tk) = S / (S / 2Vn + S / 2Vk) = 1 / (1 / 2Vn + 1 / 2Vk); 1 / Vav = 1 / 2Vn + 1 / 2Vk; 1 / 2Vc = 1 / Vcr – 1 / 2Vn = (2Vn – Vcr) / (2Vcr * Vn) and Vc = Vcr * Vn / (2Vn – Vcr).

Variables: Vav – average speed (Vav = 8 km / h); Vн – speed on the first half of the journey (Vн = 12 km / h).

Calculation: Vк = Vср * Vн / (2Vн – Vср) = 8 * 12 / (2 * 12 – 8) = 6 km / h.

Answer: In the second section, the indicated cyclist was moving at a speed of 6 km / h.