A train 350 m long is moving at the speed of 20 km/h it will cross a man coming from the opposite direction at the speed of 1 km/h in:

Options

A. 27 s
B. 35 s
C. 45 s
D. 60 s

Answer

To solve the problem of how long it will take for a train 350 meters long, moving at a speed of 20 km/h, to cross a man coming from the opposite direction at a speed of 1 km/h, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Length of the Train and the Speeds**:
- Length of the train = 350 meters
- Speed of the train = 20 km/h
- Speed of the man = 1 km/h

2. **Calculate the Relative Speed**:
- Since the train and the man are moving towards each other, their speeds will be added to find the relative speed.
- Relative speed = Speed of the train + Speed of the man
- Relative speed = 20 km/h + 1 km/h = 21 km/h

3. **Convert the Relative Speed to Meters per Second**:
- To convert km/h to m/s, we use the conversion factor: 1 km/h = (1000 m / 3600 s) = 5/18 m/s.
- Therefore, relative speed in m/s = 21 km/h × (5/18) m/s per km/h
- Relative speed = 21 × (5/18) = 35/6 m/s ≈ 5.83 m/s

4. **Use the Formula for Time**:
- The formula for time when distance and speed are known is:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
- Here, the distance is the length of the train (350 meters) and the speed is the relative speed (5.83 m/s).
- Time = 350 m / (35/6 m/s) = 350 m × (6/35) s/m = 60 seconds

5. **Conclusion**:
- The time it takes for the train to cross the man is 60 seconds.

### Final Answer:
The train will cross the man in **60 seconds**.