A train leaves Station A at 2:00 PM traveling at 80 km/h. Another train leaves Station B, 300 km away, at 3:00 PM traveling toward Station A at 100 km/h. When do they meet?

When Do Two Trains Meet? Solving a Reliable Train Encounter Problem

When two trains travel toward each other from different stations, calculating arrival time helps passengers and planners alike understand schedules and optimize travel planning. Let’s explore a classic scenario: Train A departs Station A at 2:00 PM at 80 km/h, while Train B starts from Station B—300 km away—at 3:00 PM moving toward Station A at 100 km/h. When do the trains meet?

The Problem Explained

This is a relative motion problem involving two trains moving in opposite directions. To find when and where they meet, we analyze their starting positions, speeds, and departure times carefully.

Understanding the Context

Key Details

Station A and Station B are 300 km apart.
Train A leaves Station A at 2:00 PM traveling at 80 km/h.
Train B departs Station B one hour later (at 3:00 PM) traveling at 100 km/h toward Station A.

Step-by-Step Solution

Step 1: Determine Train A’s head start
Train A begins at 2:00 PM and Travels for one full hour before Train B leaves:
Distance covered in that hour = speed × time = 80 km/h × 1 h = 80 km.

So, when Train B departs, Train A is already 80 km along the route.

A train leaves Station A at 2:00 PM traveling at 80 km/h. Another train leaves Station B, 300 km away, at 3:00 PM traveling toward Station A at 100 km/h. When do they meet?

Key Insights

Step 2: Calculate relative speed
Since both trains move toward each other, their closing speed is the sum of speeds:
80 km/h + 100 km/h = 180 km/h.

Step 3: Compute remaining distance between trains at 3:00 PM
At 3:00 PM, Train A has traveled 80 km, so the gap between them is:
300 km (total distance) − 80 km = 220 km.

Step 4: Find how long it takes to close the gap
Time = distance ÷ speed = 220 km ÷ 180 km/h = 11⁄9 hours ≈ 1 hour and 40 minutes.

Step 5: Determine meeting time
Train B starts at 3:00 PM. Adding 11⁄9 hours (1 hour 40 minutes):
3:00 PM + 1:40 = 4:40 PM.

Conclusion

The two trains meet at 4:40 PM on the way from Station A to Station B, covering the full 300 km distance through synchronized travel.

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Final Thoughts

Why This Matters

Understanding train meeting times improves scheduling efficiency, helps manage station operations, and assists passengers in planning their journeys accurately. Whether for railway logistics or curious minds, solving such puzzles reveals the power of basic physics and math in everyday transport.

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