Average speed for a round trip (different speeds) A person goes from P to Q at 5 km/h and returns from Q to P at 3 km/h. What is the average speed for the whole journey?

Introduction / Context:
For a round trip with different speeds in the two directions over the same distance, the average speed is the harmonic mean: 2uv / (u + v). It is not the arithmetic mean unless the times match, which they usually do not when speeds differ.

Given Data / Assumptions:

• Speed P→Q = 5 km/h.
• Speed Q→P = 3 km/h.
• Distances each way are equal.

Concept / Approach:
Average speed over total journey = total distance / total time. For equal distances, this simplifies to 2uv/(u+v).

Step-by-Step Solution:

Verification / Alternative check:
Assume each leg is 24 km. Times: 24/5 = 4.8 h and 24/3 = 8 h. Total distance 48 km, total time 12.8 h ⇒ 48/12.8 = 3.75 km/h.

Why Other Options Are Wrong:
4.5 and 4.25 are arithmetic-mean style answers; 4.0 is still too high.

Common Pitfalls:
Taking the simple average (5 + 3)/2 = 4, which is incorrect for average speed over equal distances.

Final Answer:
3.75 km/h