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.

Step 1: Understand the setup

• Length of each train = 500 meters
• Speeds:
  • Train A (faster) = 45 km/h
  • Train B (slower) = 30 km/h
• They are moving in opposite directions on parallel tracks.

Step 2: Convert speeds to meters per second

Speed of Train A = 45 × (1000 / 3600) = 12.5 m/s
Speed of Train B = 30 × (1000 / 3600) = 8.33 m/s

Step 3: Relative speed when moving in opposite directions = 12.5 + 8.33 = 20.83 m/s

Step 4: Since we want the slower train to pass the driver of the faster train

• Only the length of the slower train (Train B) = 500 m needs to cross the driver of Train A.

Time = Distance / Relative Speed
     = 500 / 20.83 ≈ 24 seconds

Answer: 24 seconds

The slower train will take approximately 24 seconds to pass the driver of the faster train.

This question is based on relative motion where two trains move in opposite directions. Understanding how to isolate the relevant length and apply the relative speed concept is key in such problems. Perfect for candidates preparing for competitive exams.