How many seconds will a 500 m long train take to cross a man walking with a speed of 3 km/h in the direction of the moving train, if the speed of the train is 63 km/h?

Options

A. A)25
B. B)30
C. C)40
D. D)45

Answer

To solve the problem of how many seconds a 500 m long train will take to cross a man walking at a speed of 3 km/h in the same direction as the train, which is moving at a speed of 63 km/h, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Length of the train (Distance to be covered) = 500 m
- Speed of the train = 63 km/h
- Speed of the man = 3 km/h

2. **Convert Speeds from km/h to m/s:**
- To convert km/h to m/s, we use the conversion factor \( \frac{5}{18} \).
- Speed of the train in m/s = \( 63 \times \frac{5}{18} = \frac{315}{18} = 17.5 \) m/s
- Speed of the man in m/s = \( 3 \times \frac{5}{18} = \frac{15}{18} = 0.8333 \) m/s

3. **Calculate the Relative Speed:**
- Since both the train and the man are moving in the same direction, we find the relative speed by subtracting the speed of the man from the speed of the train.
- Relative speed = Speed of the train - Speed of the man
- Relative speed = \( 17.5 \, \text{m/s} - 0.8333 \, \text{m/s} = 16.6667 \, \text{m/s} \)

4. **Use the Formula for Time:**
- The formula for time is given by:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
- Here, the distance is the length of the train (500 m) and the speed is the relative speed (16.6667 m/s).
- Time = \( \frac{500 \, \text{m}}{16.6667 \, \text{m/s}} \)

5. **Perform the Calculation:**
- Time = \( 500 \div 16.6667 \approx 30 \) seconds

### Final Answer:
The train will take approximately **30 seconds** to cross the man.

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