A bus covers the first half of a certain distance with speed v1 and the second half with a speed v2. The average speed during the whole journey is :

Average speed is defined as the total distance traveled divided by the total time taken. Let the total distance be 2d. The first half distance (d) is covered at speed v1, taking time t1 = d/v1. The second half distance (d) is covered at speed v2, taking time t2 = d/v2.

The total time T = t1 + t2 = d/v1 + d/v2 = d(v1 + v2) / (v1v2).

Average speed = Total Distance / Total Time = 2d / [d(v1 + v2) / (v1v2)].
Simplifying this, we get Average Speed = 2v1v2 / (v1 + v2).

This result is the harmonic mean of the two speeds. Option C represents the arithmetic mean, which would only be correct if the bus traveled at each speed for equal time intervals rather than equal distances.