An express train takes 4 seconds to completely enter a tunnel that is 1 km long. If it is travelling at 108 km/h, how long (in seconds) will it take to pass completely through the tunnel, from the moment the front enters until the rear leaves?

Introduction / Context:
Questions involving trains and tunnels focus on understanding how far the train must travel for its full length to clear the tunnel. Here, we are told how long the train takes just to enter the tunnel and we know the tunnel length and the train speed. From this we can deduce the train length and then compute the total time to pass through the tunnel.

Given Data / Assumptions:

• Time taken for the train to completely enter the tunnel = 4 s.
• Length of the tunnel = 1 km = 1000 m.
• Speed of the train = 108 km/h.
• The train moves at a uniform speed in a straight line.
• Total time to fully pass the tunnel is the time from when the front enters until the rear exits.

Concept / Approach:
When the train is just entering the tunnel, the distance covered in that period is equal to the length of the train itself. Once the front reaches the far end of the tunnel, the train must still move by its own length for the rear to exit. Therefore, for complete passage, the train must travel tunnel length plus its own length. We first find train length from the entry time, then use total distance and speed to find the total time.

Step-by-Step Solution:
Step 1: Convert speed to m/s: 108 km/h = 108 * 5/18 = 30 m/s. Step 2: Distance covered in 4 s while entering = speed * time = 30 * 4 = 120 m. Step 3: Therefore, length of the train = 120 m. Step 4: For complete passage, distance to be covered = tunnel length + train length = 1000 + 120 = 1120 m. Step 5: Time for full passage = total distance / speed = 1120 / 30 ≈ 37.333... s. Step 6: Rounded to two decimal places, time ≈ 37.33 seconds.

Verification / Alternative check:
We can check consistency. With a speed of 30 m/s, in 37.333... seconds, the train covers 30 * 37.333... ≈ 1120 m, which exactly equals the sum of train length and tunnel length. This confirms that our calculation is correct and matches the description of complete passage through the tunnel.

Why Other Options Are Wrong:
A time such as 33 s or 32 s would yield a shorter distance than 1120 m at 30 m/s, so the train would not yet be fully out of the tunnel. On the other hand, 40 s would imply that the train covers more distance than necessary. The option 36.43 s does not correspond to a simple fraction of 1120 / 30 and is inconsistent with the exact computation.

Common Pitfalls:
Many learners mistakenly use only the tunnel length and forget to add the train length when calculating the distance for full passage. Another error is misinterpreting the 4 seconds as the time to cross the entire tunnel, which would lead to an incorrect train length. Working carefully with distance and time relationships prevents such misunderstandings.

Final Answer:
The train will take approximately 37.33 sec to pass completely through the tunnel.