A biker goes up hill with a constant speed of 10km/h. Then he goes downhill with a constant speed of 50km/h. What's his average speed

This is not as simple as it looks.

His average speed is NOT (10km/hr + 50km/hr) / 2 = 30 km/hr.

You have to use the definition of speed:

Speed = (total distance covered) / (time to cover the distance).

Let's say the distance up (and down) the hill is 'd'.

Then the time it takes to go up the hill is (d/10) hours.

And the time it takes to come down the hill is (d/50) hours.

Total distance = 2d km

Total time = (d/10) + (d/50) = (5d/50) + (d/50) = 6d/50

Speed = distance/time = 2d / (6d/50) = 100d/6d

Speed = 100/6 = 16-2/3 km/hr