# 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.

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