A train running with a speed of 6 km/hr, crosses a telephone pole. If the length of train is 720 meters, then what is the time taken (in seconds) by the train to cross the pole?

Options

A. 430
B. 450
C. 432
D. 445

Answer

To solve the problem step by step, we need to determine how long it takes for a train to cross a telephone pole, given its speed and length. Here’s how to do it:

### Step 1: Convert the speed from km/hr to m/s
The speed of the train is given as 6 km/hr. To convert this speed into meters per second (m/s), we use the conversion factor:

\[ \text{Speed in m/s} = \text{Speed in km/hr} \times \frac{5}{18} \]

Substituting the given speed:

\[ \text{Speed in m/s} = 6 \times \frac{5}{18} = \frac{30}{18} = \frac{5}{3} \text{ m/s} \]

### Step 2: Identify the distance to be covered
The distance that the train needs to cover to completely cross the telephone pole is equal to the length of the train. The length of the train is given as 720 meters.

### Step 3: Use the formula for time
The formula for time when distance and speed are known is:

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

Substituting the values we have:

\[ \text{Time} = \frac{720 \text{ meters}}{\frac{5}{3} \text{ m/s}} \]

### Step 4: Simplify the calculation
To divide by a fraction, we multiply by its reciprocal:

\[ \text{Time} = 720 \times \frac{3}{5} \]

Calculating this gives:

\[ \text{Time} = \frac{720 \times 3}{5} = \frac{2160}{5} = 432 \text{ seconds} \]

### Conclusion
The time taken by the train to cross the telephone pole is **432 seconds**.

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