A train 110 metres long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?

Step 1: Understand the given data

• Length of the train = 110 meters
• Speed of the train = 60 km/h
• Speed of the man = 6 km/h
• The man is running in the opposite direction of the train

Step 2: Convert speeds to m/s

To convert km/h to m/s, multiply by 5/18

Speed of train = 60 × (5/18) = 16.67 m/s
Speed of man = 6 × (5/18) = 1.67 m/s

Step 3: Calculate relative speed

Since they are moving in opposite directions, relative speed = sum of their speeds

Relative speed = 16.67 + 1.67 = 18.34 m/s

Step 4: Calculate time taken to pass the man

Time = Distance / Speed = 110 / 18.34 ≈ 6 seconds

Answer: 6 seconds

The train will pass the man in approximately 6 seconds.

This problem illustrates the importance of converting units correctly and applying the concept of relative speed when two objects are moving toward or away from each other.