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?
Correct Answer: 6 km
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