Time and Distance – Two walkers, arrival-time difference: Two men walk the same distance; one 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?

Introduction / Context:
The same distance covered at different speeds yields different times. The difference in times is given, so we can write a single equation in the unknown distance and solve directly.

Given Data / Assumptions:

• Speeds = 4 km/h and 3 km/h.
• Time difference = 30 min = 0.5 h.
• Distance is common for both walkers.

Concept / Approach:
If the distance is D, then times are D/4 and D/3. The slower takes longer, so D/3 − D/4 = 0.5. Solve for D.

Step-by-Step Solution:
D/3 − D/4 = D*(1/12) = 0.5.Hence D = 0.5 * 12 = 6 km.

Verification / Alternative check:
Times: 6/4 = 1.5 h and 6/3 = 2 h; the difference is 0.5 h as required.

Why Other Options Are Wrong:
7, 8, 9, and 5 km do not produce a 0.5 h time difference at the given speeds.

Common Pitfalls:
Reversing the subtraction order or failing to convert minutes to hours.

Final Answer:
6 km