A person travels from A to B at a speed of 4 km/h and returns from B to A at a…

Concept: For a two-leg round trip where the same distance is covered at two different speeds, the average speed for the whole journey is not the arithmetic mean of the two speeds — the time spent at each speed differs. The correct measure is total distance travelled divided by total time taken, which for two equal-distance legs simplifies to the harmonic mean of the two speeds: 2 × v1 × v2 / (v1 + v2).

Application:

1. Let the one-way distance from A to B be x km.

2. Time for the outward leg at 4 km/h = x/4 hours.

3. Time for the return leg at 5 km/h = x/5 hours.

4. Total distance covered = 2x km. Total time taken = x/4 + x/5 = 9x/20 hours.

5. Average speed = total distance ÷ total time = 2x ÷ (9x/20) = 40/9 ≈ 4.44 km/h.

Cross-check: Applying the harmonic-mean formula directly: 2 × 4 × 5 / (4 + 5) = 40/9 ≈ 4.44 km/h — the same result, confirming the derivation.

Answer: 4.44 km/h.