A train runing with a speed of 45 km/hr, crosses a telephone pole. If the length of train is 810 meters, then what is the time taken (in seconds)by the train to cross the pole. ?

Options

A. 66
B. 64.8
C. 68
D. 67.2

Answer

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

### Step 1: Convert the speed from km/hr to m/s
The speed of the train is given as 45 km/hr. To convert this speed into meters per second (m/s), we use the conversion factor:
\[ \text{Speed in m/s} = \text{Speed in km/hr} \times \frac{5}{18} \]
Calculating this gives:
\[ \text{Speed} = 45 \times \frac{5}{18} = \frac{225}{18} = 12.5 \text{ m/s} \]

### Step 2: Identify the distance to be covered
When the train crosses a telephone pole, the distance it needs to cover is equal to its own length. The length of the train is given as 810 meters. Therefore, the distance \(d\) is:
\[ d = 810 \text{ meters} \]

### Step 3: Use the formula for time
The time taken \(t\) to cross the pole can be calculated using the formula:
\[ t = \frac{d}{\text{speed}} \]
Substituting the values we have:
\[ t = \frac{810 \text{ meters}}{12.5 \text{ m/s}} \]

### Step 4: Calculate the time
Now, we perform the division:
\[ t = \frac{810}{12.5} = 64.8 \text{ seconds} \]

### Conclusion
The time taken by the train to cross the telephone pole is **64.8 seconds**.