A 110 m long train crosses a tree in 3 seconds. How long will it take to cross a 165 m long platform and a 135 m long bridge that are separated by 30 m of track (i.e., there is a 30 m gap between the platform and the bridge)?

Introduction / Context:
Speed from the tree-crossing gives us the train’s speed. To clear two separate structures with a 30 m gap, the front of the train must travel the platform length + gap + bridge length + one train length to ensure the rear leaves the far end of the bridge.

Given Data / Assumptions:

• Train length L = 110 m
• Time to pass tree = 3 s ⇒ speed = L / 3 m/s
• Platform = 165 m, Bridge = 135 m, Gap = 30 m

Concept / Approach:
When clearing sequential structures with a separation, the required head travel distance from first contact to final clearance is (platform + gap + bridge + L). Time = distance / speed.

Step-by-Step Solution:

Verification / Alternative check:
Single-structure checks: clearing S requires S + L distance; with two structures and a gap, distances add linearly, yielding 440 m total.

Why Other Options Are Wrong:

• 15, 16, 18 s do not match 440 / (110/3).

Common Pitfalls:

• Adding an extra train length for the platform unnecessarily (double-counting).
• Using average instead of exact speed from the tree crossing.

Final Answer:
12 s