A 100 m long train is running at a speed of 68 km/h. A man is also running in the same
direction with a speed of 8 km/h. In what time will the train overtake the running man?
A. 6 sec
B. 9 sec
C. 6 min
D. 9 min

Problem Breakdown

You are given:

• Length of the train = 100 meters
• Speed of the train = 68 km/h
• Speed of the man = 8 km/h

Both are moving in the same direction.

Step-by-Step Solution

Step 1: Convert speeds to the same unit

Convert the speeds from km/h to m/s:

Speed (m/s) = Speed (km/h) × (1000 / 3600)

• Train: 68 × (1000 / 3600) = 18.89 m/s
• Man: 8 × (1000 / 3600) = 2.22 m/s

Step 2: Use Relative Speed

Since they are moving in the same direction:

Relative Speed = Train Speed – Man Speed = 18.89 – 2.22 = 16.67 m/s

Step 3: Use Time = Distance / Speed

Time = 100 / 16.67 = 6 seconds (approx)

✅ Correct Answer: A. 6 sec

Key Takeaways

• Always convert to consistent units (like m/s).
• Use relative speed for objects moving in the same direction.
• This formula is super helpful in speed-distance-time based reasoning problems.