Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 5 seconds. What is the length of the fast train?

Given Data

• Speeds of two trains in the same direction = 40 km/hr and 20 km/hr
• Time taken for the fast train to completely pass a man in the slower train = 5 s
• Required: length of the fast train

Step 1: Use relative speed for same direction
Relative speed = 40 − 20 = 20 km/hrConvert to m/s: 20 × (1000/3600) = 20 × (5/18) = 5.5556 m/s

Step 2: Distance covered while passing the man equals length of the fast train
Length L = relative speed × timeL = 5.5556 × 5 = 27.7778 mRounded to two decimals: L = 27.78 m

Checks & Common Pitfalls

• For the same direction, take the difference of speeds, not the sum.
• When a train passes a standing man or a man moving with the other train, the distance equals only the length of the passing train.
• Use consistent units; convert km/hr to m/s by multiplying by 5/18.

Final Answer
The length of the fast train is 27.78 m.