Problems on Trains – Tunnel length from total crossing time: A 400 m long train running at 54 km/h (constant speed) crosses a tunnel in 2 minutes. What is the tunnel’s length?

Introduction / Context:Passing completely through a tunnel requires the train to cover its own length plus the tunnel length. With speed and total time known, compute the total distance; subtract the train length to obtain the tunnel length.

Given Data / Assumptions:

• L_train = 400 m.
• Speed = 54 km/h = 15 m/s.
• Time = 2 minutes = 120 s.

Concept / Approach:Total distance = speed * time; then L_tunnel = total distance − L_train.

Step-by-Step Solution:Total distance = 15 * 120 = 1800 m.Tunnel length = 1800 − 400 = 1400 m.

Verification / Alternative check:At 15 m/s, 1400 m takes 93.33 s; with 400 m more (train length), additional 26.67 s; sum 120 s, confirming the calculation.

Why Other Options Are Wrong:1200, 1600, 1800, 1000 m do not satisfy the total distance constraint with the given speed and time.

Common Pitfalls:Using tunnel length alone for distance; not converting time to seconds or speed to m/s.

Final Answer:1400 m