A train of length 218 m is running at 60 km/h .In what time (in seconds ) will it cross a platform of length 282 m?

Options

A. 30
B. 32
C. 40
D. 36

Answer

To solve the problem of how long it takes for a train to cross a platform, we can follow these steps:

### Step 1: Understand the Problem
The train has a length of 218 meters and is moving at a speed of 60 km/h. The platform has a length of 282 meters. To find out how long it takes for the train to completely cross the platform, we need to calculate the total distance the train must cover, which is the sum of the lengths of the train and the platform.

### Step 2: Calculate the Total Distance
The total distance \( D \) that the train needs to cover to completely cross the platform is given by:
\[ D = \text{Length of Train} + \text{Length of Platform} \]
Substituting the values:
\[ D = 218 \, \text{m} + 282 \, \text{m} = 500 \, \text{m} \]

### Step 3: Convert Speed from km/h to m/s
The speed of the train is given in kilometers per hour (km/h). We need to convert this speed into meters per second (m/s) for our calculations. The conversion formula is:
\[ \text{Speed in m/s} = \text{Speed in km/h} \times \frac{1000}{3600} \]
Substituting the given speed:
\[ \text{Speed} = 60 \, \text{km/h} \times \frac{1000}{3600} = \frac{60000}{3600} = \frac{600}{36} = 16.67 \, \text{m/s} \]

### Step 4: Calculate the Time Taken to Cross the Platform
Now, we can find the time \( t \) taken to cross the platform using the formula:
\[ t = \frac{D}{\text{Speed}} \]
Substituting the values we calculated:
\[ t = \frac{500 \, \text{m}}{16.67 \, \text{m/s}} \approx 30 \, \text{seconds} \]

### Final Answer
The time taken for the train to cross the platform is approximately **30 seconds**.

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