Opposite-running trains with a staggered start — meeting place & time: The distance between stations X and Y is 450 km. Train L leaves X at 6:00 pm at 60 km/h. Train M leaves Y earlier at 5:20 pm at 80 km/h. When and where (from X) do they meet?

Introduction / Context:
Meeting problems with staggered departures are solved by accounting for one train’s head start, then using relative speed thereafter.

Given Data / Assumptions:

• Distance X–Y = 450 km
• Train L: 60 km/h, starts 6:00 pm from X
• Train M: 80 km/h, starts 5:20 pm from Y (40 min earlier)

Concept / Approach:
Compute distance M covers before 6:00 pm, subtract from 450, then divide by relative speed (60 + 80) for the time after 6:00 pm.

Step-by-Step Solution:

Verification / Alternative check:
Check M’s distance from Y at 8:50 pm: 80 * (3 h 30 min) = 280 km; sums with 170 km to 450 km.

Why Other Options Are Wrong:
They place the meet too early/late or at the wrong distance given the head start.

Common Pitfalls:
Forgetting to include the early start distance or using only one train’s speed instead of the relative speed.

Final Answer:
170 km, 8 : 50 pm