Two trains 132 m and 108 m long run in opposite directions at 32 km/h and 40 km/h, respectively. From the moment they meet, how many seconds do they take to cross each other completely?

Introduction / Context:For trains moving in opposite directions, the total distance to clear is the sum of lengths; the relative speed is the sum of speeds. Time equals distance over relative speed with consistent units.

Given Data / Assumptions:

• L1 = 132 m; L2 = 108 m; total = 240 m.
• Speeds = 32 km/h and 40 km/h → combined = 72 km/h.

Concept / Approach:Convert 72 km/h to m/s, then compute time = 240 / (relative speed in m/s).

Step-by-Step Solution:72 km/h = 20 m/s.t = 240 / 20 = 12 s.

Verification / Alternative check:In 12 s at 20 m/s, the combined distance is 240 m, exactly the sum of lengths.

Why Other Options Are Wrong:10, 11, 13 s do not match 240 m at 20 m/s.

Common Pitfalls:Using difference of speeds (for same direction) instead of sum for opposite directions.

Final Answer:12 seconds