A person goes from Kalyan-Dombivli to Rajkot at a speed of 3 km/hr and returns…

When a journey covers the same distance in each direction at two different speeds, the average speed for the whole trip is the harmonic mean of the two speeds, not their arithmetic mean: Average speed = 2v1v2 / (v1 + v2). This is because average speed is always total distance divided by total time, and equal distances at unequal speeds take unequal times.

1. Let the one-way distance between Kalyan-Dombivli and Rajkot be d km.

2. Time for the onward leg at 3 km/hr = d/3 hours.

3. Time for the return leg at 6 km/hr = d/6 hours.

4. Total distance for the round trip = d + d = 2d km.

5. Total time taken = d/3 + d/6 = 2d/6 + d/6 = 3d/6 = d/2 hours.

6. Average speed = Total distance ÷ Total time = 2d ÷ (d/2) = 4 km/hr.

Cross-check with a convenient distance, say d = 6 km: onward time = 6/3 = 2 hours, return time = 6/6 = 1 hour, total distance = 12 km, total time = 3 hours, so average speed = 12/3 = 4 km/hr — the same result.

This confirms the average speed for the entire journey is 4 km/hr.