Head-on trains – time to clear each other Two trains of lengths 132 m and 108 m run towards each other on parallel tracks at 32 km/h and 40 km/h respectively. How many seconds from meeting until they are clear?

Introduction / Context:When two trains approach head-on, use relative speed. The time from the instant their fronts meet until they are clear equals (sum of lengths)/(relative speed).

Given Data / Assumptions:

• L1 = 132 m, L2 = 108 m.
• Speeds: 32 km/h and 40 km/h (uniform).

Concept / Approach:Relative speed for opposite directions is v1 + v2. Convert to m/s, then apply t = (L1 + L2)/v_rel.

Step-by-Step Solution:

Verification / Alternative check:Reverse: 12 s * 20 m/s = 240 m, which matches the sum of lengths.

Why Other Options Are Wrong:9 s → 180 m; 15 s → 300 m; neither equals 240 m. “Data inadequate” is incorrect; we have all needed data.

Common Pitfalls:Forgetting to add speeds for opposite directions or failing to convert km/h to m/s before using meters and seconds.

Final Answer:12 sec