An 800 m long train is moving at 63 km/h and a man is walking at 3 km/h in the same direction along the track. How many seconds will the train take to completely cross the man?

Introduction / Context:
This question tests understanding of relative speed in the same direction between a fast-moving train and a walking man. The train must cover its entire length relative to the man in order to completely cross him. The problem requires correct use of relative speed, unit conversion from km/h to m/s and then finding the time using distance and speed.

Given Data / Assumptions:

• Length of train = 800 m.
• Speed of train = 63 km/h.
• Speed of man = 3 km/h.
• Both are moving in the same direction.
• Speeds are constant.

Concept / Approach:
When two objects move in the same direction, their relative speed is the difference between their speeds. The effective speed at which the train draws away from the man is (63 - 3) km/h. We convert this relative speed to m/s and then use time = distance / speed, where the distance is the length of the train, because the train must cover its own length relative to the man to cross him completely.

Step-by-Step Solution:
Relative speed = 63 - 3 = 60 km/h. Convert 60 km/h to m/s: 60 * 1000 / 3600 = 60 * 5 / 18 = 50 / 3 m/s. Distance to be covered relative to the man = length of train = 800 m. Time taken = distance / relative speed. Time = 800 / (50 / 3) = 800 * 3 / 50 = 2400 / 50 = 48 seconds.

Verification / Alternative check:
At a relative speed of 50 / 3 m/s, in 48 seconds the distance covered = (50 / 3) * 48 = 50 * 16 = 800 m, exactly the length of the train. This confirms that 48 seconds is the correct time for complete crossing.

Why Other Options Are Wrong:

• 52, 38 and 42 seconds all give distances different from 800 m when multiplied by the relative speed of 50 / 3 m/s.

Common Pitfalls:
Common mistakes include adding the speeds instead of subtracting them when motion is in the same direction, and incorrect conversion between km/h and m/s. Some candidates also forget that the whole length of the train has to pass the man, not just its front end, leading to incorrect use of distance.

Final Answer:
The train will take 48 seconds to completely cross the man.