How many seconds will a 500 metre long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?

Step 1: Understand what's given

• Length of the train = 500 meters
• Speed of the train = 63 km/h
• Speed of the man = 3 km/h
• The man is walking in the same direction as the train.

Step 2: Use relative speed

When two objects move in the same direction, we subtract their speeds:

Relative speed = 63 - 3 = 60 km/h
Convert to m/s: 60 × (1000 / 3600) = 60 × 5/18 = 16.67 m/s

Step 3: Calculate time to cross

Time = Distance / Speed

Time = 500 / 16.67 ≈ 30 seconds

Answer: The train will take approximately 30 seconds to cross the man.

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This problem is a classic example of relative motion, where:

• Same direction → subtract speeds
• Opposite direction → add speeds

These concepts are frequently tested in competitive exams and aptitude sections.