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?

Given Data

• Train length = 500 m
• Speed of train = 63 km/hr
• Speed of man = 3 km/hr
• Both move in the same direction

Step 1: Compute relative speed (same direction) Relative speed = Speed of train − Speed of man = 63 − 3 = 60 km/hr

Step 2: Convert relative speed to m/s 1 km/hr = 5/18 m/s Relative speed = 60 × (5/18) = 50/3 m/s ≈ 16.67 m/s

Step 3: Distance to be covered When a train crosses a man (a point), the distance = length of train = 500 m

Step 4: Time = Distance ÷ Speed Time = 500 ÷ (50/3) = 500 × 3 ÷ 50 = 30 seconds

Sanity Check (all in km and hours) Train length = 500 m = 0.5 km Time (hours) = 0.5 ÷ 60 = 1/120 hour Time (seconds) = (1/120) × 3600 = 30 seconds

Final Answer The required time is 30 seconds.