A train of length 120 m travels at a speed of 57 km/h. In what time it will pass a man who is walking at 3 km/h in the opposite direction?

Explanation

To solve the problem of how long it takes for a train to pass a man walking in the opposite direction, we can follow these steps:

### Step 1: Identify the given data
- Length of the train (L) = 120 m
- Speed of the train (V_train) = 57 km/h
- Speed of the man (V_man) = 3 km/h

### Step 2: Convert the speeds from km/h to m/s
To convert km/h to m/s, we use the conversion factor:
\[ 1 \text{ km/h} = \frac{5}{18} \text{ m/s} \]

- Speed of the train in m/s:
\[ V_{train} = 57 \text{ km/h} \times \frac{5}{18} = \frac{285}{18} \text{ m/s} = 15.83 \text{ m/s} \]

- Speed of the man in m/s:
\[ V_{man} = 3 \text{ km/h} \times \frac{5}{18} = \frac{15}{18} \text{ m/s} = 0.83 \text{ m/s} \]

### Step 3: Calculate the relative speed
Since the train and the man are moving in opposite directions, we add their speeds to find the relative speed:
\[ V_{relative} = V_{train} + V_{man} = 15.83 \text{ m/s} + 0.83 \text{ m/s} = 16.66 \text{ m/s} \]

### Step 4: Calculate the time taken to pass the man
The time taken (t) for the train to pass the man can be calculated using the formula:
\[ t = \frac{\text{Distance}}{\text{Speed}} \]
Here, the distance is the length of the train (120 m):
\[ t = \frac{120 \text{ m}}{16.66 \text{ m/s}} \approx 7.20 \text{ seconds} \]

### Final Answer
The time taken for the train to pass the man is approximately **7.20 seconds**.

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