X and Y start toward each other at 8:00 a.m. from points 17.5 km apart. Speeds: X = 3 km/h, Y = 4 km/h. At what time do they meet?

Introduction / Context:
The classic meeting-time problem: when two objects move toward each other, add their speeds to get the closing rate. Time to meet = distance / (sum of speeds). Add this time to the start time to get the clock time.

Given Data / Assumptions:

• Initial separation = 17.5 km.
• Speeds: 3 km/h and 4 km/h.
• Start time = 8:00 a.m.

Concept / Approach:
Closing speed = 3 + 4 = 7 km/h. Time in hours = 17.5 / 7 = 2.5 h.

Step-by-Step Solution:

Verification / Alternative check:
Distances covered: X → 3 * 2.5 = 7.5 km; Y → 4 * 2.5 = 10 km; total 17.5 km.

Why Other Options Are Wrong:
11:30 a.m./p.m. are an hour late; p.m. variants misplace time of day.

Common Pitfalls:
Forgetting to add speeds or mis-converting 0.5 h to 30 min.

Final Answer:
10 : 30 am