Mr Tortoise completes the race at an average speed of 20 km/hr. His average speed for the first two stretches is four times that for the last stretch. Find the speed over stretch C.

Average speed to cover complete race = 20 km/hr = $$\frac{2+2+2}{t_1 + t_2 + t_3}$$ (Where $$t_1$$ is time taken to cover the distance A, $$t_2$$ is time taken to cover the distance B and $$t_3$$ is time taken to cover the distance C)

So total time =$$ t_1 + t_2 + t_3 = 18$$ min.

Avg. speed for first two streches = $$\frac{4}{t_1 + t_2}$$

Avg. speed for last strech = $$\frac{2}{t_3}$$

Given: $$\frac{4}{t_1 + t_2} = 4 \times \frac{2}{t_3}$$

Or $$2t_1 + 2t_2 = t_3$$

Or $$t_3 = 12$$ min.

So $$V_3 = \frac{2}{12} \times 60$$ = 10 km/hr