Average Speed – Two equal halves at 6 km/h and 3 km/h: A man covers half his journey at 6 km/h and the remaining half at 3 km/h. What is his average speed for the whole journey?

Introduction / Context:
For equal distances at two speeds, average speed is the harmonic mean. Direct averaging of speeds is invalid because the slower portion consumes more time.

Given Data / Assumptions:

• First half speed = 6 km/h.
• Second half speed = 3 km/h.
• Distances of both halves are equal.

Concept / Approach:
Average speed over equal distances = 2ab / (a + b). Here a = 6 and b = 3.

Step-by-Step Solution:
Average speed = 2*6*3 / (6 + 3) = 36/9 = 4 km/h.

Verification / Alternative check:
Let each half be 9 km. Times are 9/6 = 1.5 h and 9/3 = 3 h; total time = 4.5 h for 18 km ⇒ 18/4.5 = 4 km/h.

Why Other Options Are Wrong:
3 or 4.5 km/h are arithmetic means of parts or times misapplied; 9 km/h is the maximum leg speed not the round-trip average.

Common Pitfalls:
Using the arithmetic mean ( (6 + 3)/2 = 4.5 ) rather than the harmonic mean.

Final Answer:
4 km/h