A train 100 metres long travels at 70 km per hour.A man is running at 10 km per hour in the same direction in which the train is going .The train will pass the man in -----

Options

A. 6 seconds
B. 6 2/3 seconds
C. 7 seconds
D. 8 seconds

Answer

To solve the problem, we need to determine how long it takes for a train that is 100 meters long, traveling at 70 km/h, to pass a man running at 10 km/h in the same direction.

### Step-by-Step Solution:

1. **Identify the Length of the Train:**
- The length of the train is given as 100 meters.

2. **Determine the Speeds:**
- Speed of the train = 70 km/h
- Speed of the man = 10 km/h

3. **Calculate the Relative Speed:**
- Since both the train and the man are moving in the same direction, the relative speed is the difference between their speeds.
\[ \text{Relative Speed} = \text{Speed of Train} - \text{Speed of Man} = 70 \text{ km/h} - 10 \text{ km/h} = 60 \text{ km/h} \]

4. **Convert the Relative Speed to Meters per Second:**
- To convert km/h to m/s, use the conversion factor \( \frac{5}{18} \).
\[ \text{Relative Speed in m/s} = 60 \text{ km/h} \times \frac{5}{18} = \frac{300}{18} = \frac{50}{3} \text{ m/s} \]

5. **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 (100 meters) and the speed is the relative speed (\(\frac{50}{3}\) m/s).
\[ \text{Time} = \frac{100 \text{ meters}}{\frac{50}{3} \text{ m/s}} = 100 \times \frac{3}{50} = 6 \text{ seconds} \]

6. **Conclusion:**
- The time taken for the train to pass the man is 6 seconds.

### Final Answer:
The train will pass the man in **6 seconds**.

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