A 440 m long train runs at 240 km/h. In the opposite direction, a man runs at 24 km/h. In what time will the train completely pass the man?

Introduction / Context:When two objects approach each other, relative speed is the sum of their speeds. For a train crossing a man, the distance to be covered is just the train’s length. Compute relative speed, convert units, then apply time = distance / speed.

Given Data / Assumptions:

• Train length L = 440 m.
• Train speed = 240 km/h.
• Man speed (opposite) = 24 km/h.

Concept / Approach:v_rel = (240 + 24) km/h = 264 km/h. Convert to m/s via 5/18; then t = L / v_rel.

Step-by-Step Solution:

Verification / Alternative check:In 6 s at 73.333... m/s, the train covers 440 m exactly, so it clears the man.

Why Other Options Are Wrong:4 s needs 110 m/s; 9 s implies 48.9 m/s; 12 s means 36.7 m/s. None match 73.333... m/s.

Common Pitfalls:Using speed difference instead of sum for opposite directions or skipping unit conversion.

Final Answer:6 s