A train 200 m long travels at the speed of 72 km/h A man is runing at 3.6 km/h in the same direction in which train is going.The train will pass the man is:

Options

A. 10 s
B. 12(3/19)s
C. 10(10/19)s
D. none of these

Answer

To solve the problem of how long it will take for a train to pass a man running in the same direction, we can follow these steps:

### Step 1: Convert the speeds from km/h to m/s
The speed of the train is given as 72 km/h and the speed of the man is 3.6 km/h. To convert these speeds into meters per second (m/s), we use the conversion factor \( \frac{5}{18} \).

- Speed of the train in m/s:
\[ \text{Speed of train} = 72 \times \frac{5}{18} = 20 \text{ m/s} \]

- Speed of the man in m/s:
\[ \text{Speed of man} = 3.6 \times \frac{5}{18} = 1 \text{ m/s} \]

### Step 2: Calculate the relative speed
Since both the train and the man are moving in the same direction, the relative speed of the train with respect to the man is:
\[ \text{Relative speed} = \text{Speed of train} - \text{Speed of man} = 20 \text{ m/s} - 1 \text{ m/s} = 19 \text{ m/s} \]

### Step 3: Determine the distance to be covered
The length of the train is given as 200 meters. This is the distance the train needs to cover to completely pass the man.

### Step 4: Calculate the time taken to pass the man
Using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
we can substitute the values we have:
\[ \text{Time} = \frac{200 \text{ m}}{19 \text{ m/s}} \approx 10.53 \text{ seconds} \]

### Step 5: Round off the time
Since the question might require a rounded answer, we can round 10.53 seconds to 11 seconds.

### Final Answer
The train will pass the man in approximately **11 seconds**.

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