Question

A train 110 metres long is running with a speed of 60kmph. 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?

• A. Ssec
• B. 6sec
• C. 10sec
• D. 15sec
• E. 12sec

Answer 1

The Correct Option is B

The correct answer is option (B):

6sec

Here's how to solve this problem:

1. **Understand Relative Speed:** When two objects are moving towards each other (in opposite directions), their speeds add up to determine how quickly they are closing the distance between them. In this case, the train and the man are moving towards each other.

2. **Calculate Relative Speed:**
* Train's speed: 60 kmph
* Man's speed: 6 kmph
* Relative speed = Train's speed + Man's speed = 60 kmph + 6 kmph = 66 kmph

3. **Convert to Meters per Second:** To have consistent units, we need to convert the relative speed from kilometers per hour to meters per second. The conversion factor is 1 kmph = 5/18 m/s.
* Relative speed = 66 kmph * (5/18) m/s/kmph = 55/3 m/s (approximately 18.33 m/s)

4. **Determine Distance:** The distance the train needs to cover to pass the man is the length of the train itself, which is 110 meters.

5. **Calculate Time:** Time = Distance / Speed
* Time = 110 meters / (55/3 m/s)
* Time = 110 meters * (3/55 s/m)
* Time = 6 seconds

Therefore, the train will pass the man in 6 seconds.