A train crosses a pole in 15 seconds when it is moving at 20 m/s. Find the time taken by the train to cross a platform 600 m long.

Options

A. 40s
B. 1min
C. 45s
D. 3min

Answer

To solve the problem step by step, we will follow these steps:

### Step 1: Calculate the Length of the Train
When the train crosses a pole, it travels a distance equal to its own length. We can calculate the length of the train using the formula:

\[ \text{Distance} = \text{Speed} \times \text{Time} \]

Given that the speed of the train is 20 m/s and the time taken to cross the pole is 15 seconds, we can substitute these values into the formula:

\[ \text{Length of the Train} = 20 \, \text{m/s} \times 15 \, \text{s} = 300 \, \text{m} \]

### Step 2: Calculate the Total Distance to Cross the Platform
When the train crosses a platform, it needs to cover the length of the train plus the length of the platform. The length of the platform is given as 600 m. Therefore, the total distance the train needs to cover is:

\[ \text{Total Distance} = \text{Length of the Train} + \text{Length of the Platform} \]

Substituting the values we have:

\[ \text{Total Distance} = 300 \, \text{m} + 600 \, \text{m} = 900 \, \text{m} \]

### Step 3: Calculate the Time Taken to Cross the Platform
Now that we have the total distance the train needs to cover to cross the platform, we can calculate the time taken using the same formula as before:

\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

Substituting the total distance and the speed of the train:

\[ \text{Time} = \frac{900 \, \text{m}}{20 \, \text{m/s}} = 45 \, \text{s} \]

### Final Answer
The time taken by the train to cross the platform is **45 seconds**.

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