Two goods train each 500 m long, are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one.

Given Data

• Length of each train = 500 m
• Speed of faster train = 45 km/hr
• Speed of slower train = 30 km/hr
• Opposite directions ⇒ speeds add up for relative motion
• Passing the driver (a point) ⇒ distance to be covered = length of the slower train only = 500 m

Step 1: Convert relative speed to m/s Relative speed = 45 + 30 = 75 km/hr 1 km/hr = 5/18 m/s Relative speed = 75 × (5/18) = 375/18 = 125/6 m/s ≈ 20.833 m/s

Step 2: Time = Distance ÷ Speed Distance to pass the driver = 500 m Time = 500 ÷ (125/6) = 500 × 6 / 125 = 24 seconds

Final Answer The slower train takes 24 seconds to pass the driver of the faster train.