A train 120 m long runs at a uniform speed of 54 km/h (i.e., 15 m/s). How much time will it take to completely cross a tunnel that is 130 m long? (Assume the train must clear its entire length past the tunnel.)

Introduction / Context:This is a standard trains-and-platforms problem involving uniform motion, unit conversion from km/h to m/s, and the idea that a train must cover its own length plus the obstacle length to completely cross it.

Given Data / Assumptions:

• Train length L_t = 120 m.
• Tunnel length L_p = 130 m.
• Speed v = 54 km/h = 15 m/s.
• Uniform speed; ignore acceleration and reaction time.

Concept / Approach:To clear the tunnel, the train’s front must move a distance equal to (train length + tunnel length). Time = total distance / speed with consistent units.

Step-by-Step Solution:

Verification / Alternative check:If time were 15 s, distance covered = 15 * 15 = 225 m, which is not enough to clear 250 m. Hence 50/3 s is consistent.

Why Other Options Are Wrong:12 s and 15 s are too short for 250 m at 15 m/s; 20 s is longer than necessary; only 50/3 s exactly fits 250/15.

Common Pitfalls:Forgetting to add both lengths or failing to convert km/h to m/s correctly.

Final Answer:50/3 seconds