What is the time taken by a 180 m long train running at 54 km/h to cross a man standing on a platform ?

Answer

To solve the problem of how long it takes for a 180 m long train running at 54 km/h to cross a man standing on a platform, we can follow these steps:

### Step 1: Understand the Problem
We need to find the time taken by the train to completely pass the man. The length of the train is 180 meters, and the speed of the train is given in kilometers per hour.

### Step 2: Convert Speed to Meters per Second
Since the distance is in meters, we should convert the speed from kilometers per hour to meters per second. The conversion factor is:
\[ 1 \text{ km/h} = \frac{5}{18} \text{ m/s} \]
Thus, we convert 54 km/h:
\[ 54 \text{ km/h} = 54 \times \frac{5}{18} \text{ m/s} \]
Calculating this:
\[ 54 \times \frac{5}{18} = 15 \text{ m/s} \]

### Step 3: 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 (180 m) and the speed is 15 m/s.

### Step 4: Calculate the Time
Substituting the values into the formula:
\[ \text{Time} = \frac{180 \text{ m}}{15 \text{ m/s}} \]
Calculating this gives:
\[ \text{Time} = 12 \text{ seconds} \]

### Conclusion
The time taken by the train to cross the man standing on the platform is **12 seconds**.

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