Towns A and B are connected. Mr. Faruqui cycles from A to B at 16 km/h and then returns from B to A on foot at 9 km/h, covering the same distance each way. What is his average speed for the entire round trip?

Introduction / Context:For equal distances out and back at speeds v1 and v2, the average speed is the harmonic mean: V = 2*v1*v2 / (v1 + v2). This arises from total distance divided by total time.

Given Data / Assumptions:

• v1 = 16 km/h (A to B), v2 = 9 km/h (B to A).
• Distances on both legs are equal.

Concept / Approach:Apply the harmonic-mean formula directly for two equal-distance legs.

Step-by-Step Solution:

Verification / Alternative check:Let one-way distance be D: total time = D/16 + D/9 = (25D/144). Average = total distance (2D) / time = 2D / (25D/144) = 288/25.

Why Other Options Are Wrong:They contradict the exact harmonic mean for v1 = 16 and v2 = 9.

Common Pitfalls:Taking the arithmetic mean (12.5) instead of using total-time logic for equal distances.

Final Answer:11.52 km/h