A train 180m long moving at the speed of 20m/sec over -takes a man moving at a speed of 10m/sec in the same direction. The train passes the man in

Options

A. 6 sec
B. 9sec
C. 18sec
D. 27sec

Answer

To solve the problem, we need to determine how long it takes for the train to completely pass the man. We can use the formula for time, which is:

\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

### Step-by-Step Solution:

1. **Identify the Length of the Train**:
The length of the train is given as 180 meters.

2. **Determine the Speeds**:
- Speed of the train = 20 m/s
- Speed of the man = 10 m/s

3. **Calculate the Relative Speed**:
Since both the train and the man are moving in the same direction, we need to find the relative speed of the train with respect to the man:
\[ \text{Relative Speed} = \text{Speed of Train} - \text{Speed of Man} = 20 \, \text{m/s} - 10 \, \text{m/s} = 10 \, \text{m/s} \]

4. **Use the Distance to Find Time**:
The time taken for the train to completely pass the man can be calculated using the distance (length of the train) and the relative speed:
\[ \text{Time} = \frac{\text{Distance}}{\text{Relative Speed}} = \frac{180 \, \text{m}}{10 \, \text{m/s}} = 18 \, \text{seconds} \]

### Final Answer:
The train passes the man in **18 seconds**.

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