A boy goes from his village to school at 3 km/h and returns at 2 km/h. If the total time for the round trip is 5 hours, what is the one-way distance between the village and the school?

Introduction / Context:
For out-and-back journeys with different speeds over the same distance, total time is the sum of the two leg times using the same one-way distance.

Given Data / Assumptions:

• Forward speed = 3 km/h; return speed = 2 km/h.
• Total time (to and fro) = 5 h.
• Let one-way distance be D km.

Concept / Approach:
Total time = D/3 + D/2. Solve for D.

Step-by-Step Solution:

Verification / Alternative check:
Times: 6/3 = 2 h out; 6/2 = 3 h back; total = 5 h as given.

Why Other Options Are Wrong:
They do not satisfy the exact time equation with the stated speeds.

Common Pitfalls:
Using average speed naively (e.g., arithmetic mean) instead of computing time per leg and summing.

Final Answer:
6 km