Two men walk a fixed distance. One walks at 4 km/h and the other at 3 km/h. The faster man arrives 30 minutes earlier than the slower. What is the distance (in km)?

Introduction / Context:
For the same distance covered at two different speeds, the time difference equals distance * (1/v2 - 1/v1). Given the time gap is half an hour, we can solve for the distance directly.

Given Data / Assumptions:

• Speeds: 4 km/h (faster) and 3 km/h (slower).
• Time difference = 0.5 h.
• Distance is the same for both.

Concept / Approach:
Let distance be D. Then D/3 - D/4 = 0.5. Solve for D using fractions or a common denominator. Keep units in hours and kilometres.

Step-by-Step Solution:

Verification / Alternative check:
Time at 4 km/h: 6 / 4 = 1.5 h. Time at 3 km/h: 6 / 3 = 2 h. Difference = 0.5 h, which matches.

Why Other Options Are Wrong:
7, 8, and 9 km produce time gaps of 0.292, 0.333, and 0.375 h respectively, not 0.5 h.

Common Pitfalls:
Reversing faster and slower times or using the difference of speeds instead of the difference of reciprocal speeds.

Final Answer:
6 km