Problems on Trains – Train + platform crossing time (speed and lengths given): A train is running at 264 km/h. If the train length is 330 m and the platform length is 330 m, how long (in seconds) will the train take to completely cross the platform?

Introduction / Context:
In platform-crossing problems, the train must cover its own length plus the platform length. With a given speed, time is distance divided by speed after converting all units consistently to SI (metres and seconds).

Given Data / Assumptions:

• Train speed = 264 km/h.
• Train length = 330 m.
• Platform length = 330 m.
• Motion is uniform and straight, with no acceleration phases.

Concept / Approach:
Total distance to clear the platform = L_train + L_platform. Convert speed from km/h to m/s using 1 km/h = 5/18 m/s. Then compute time = distance / speed in seconds.

Step-by-Step Solution:
Total distance = 330 + 330 = 660 m.Speed (m/s) = 264 * (5/18) = 73.333… m/s.Time = 660 / 73.333… = 9 s.

Verification / Alternative check:
Quick ratio check: 73.333 m each second; in 9 s, distance covered = 660 m, exactly the required sum of lengths.

Why Other Options Are Wrong:
11 s, 12 s, and 15 s overestimate the time (would imply lower speeds than 264 km/h). 8 s would cover only ~586.7 m, insufficient to clear both lengths.

Common Pitfalls:
Forgetting to add train and platform lengths; mixing units by using km and m together; converting 264/3.6 incorrectly.

Final Answer:
9 sec