X and Y start walking toward each other at 8:00 am from points 17.5 km apart. Their speeds are 3 km/h and 4 km/h, respectively. At what time do they meet?
Aptitude
Time and Distance
Difficulty: Easy
Choose an option
Answer
Correct Answer: 10 : 30 am
Explanation
Introduction / Context:When two people move toward each other on a line, the closing speed is the sum of their speeds. Divide the initial separation by the closing speed to get the meeting time from the start.
Given Data / Assumptions:
- Distance apart = 17.5 km.
- Speeds: 3 km/h and 4 km/h.
- Start time = 8:00 am.
Concept / Approach:Relative (closing) speed = 3 + 4 = 7 km/h. Time to meet = distance / relative speed.
Step-by-Step Solution:
Time = 17.5 / 7 = 2.5 hours = 2 h 30 min.Meeting time = 8:00 am + 2 h 30 min = 10:30 am.Verification / Alternative check:Positions after 2.5 h: X covers 7.5 km, Y covers 10 km; total 17.5 km—consistent.
Why Other Options Are Wrong:Evening times are impossible here; 11:30 am implies 3.5 hours instead of 2.5.
Common Pitfalls:Using the difference of speeds instead of the sum for opposite directions.
Final Answer:10 : 30 am