A train 550 metres long is running with a speed of 55 km per hour .In what time will it pass a signal post ?

Options

A. 30 sec
B. 24 sec
C. 42 sec
D. 36 sec

Answer

To solve the problem of how long it takes for a train 550 meters long to pass a signal post while traveling at a speed of 55 km/h, we can follow these steps:

### Step 1: Identify the given values
- Length of the train (Distance to cover) = 550 meters
- Speed of the train = 55 km/h

### Step 2: Convert the speed from km/h to m/s
To convert the speed from kilometers per hour to meters per second, we use the conversion factor:
\[ 1 \text{ km/h} = \frac{5}{18} \text{ m/s} \]
Thus,
\[ \text{Speed in m/s} = 55 \times \frac{5}{18} \]

### Step 3: Calculate the speed in m/s
Calculating the speed:
\[ \text{Speed in m/s} = 55 \times \frac{5}{18} = \frac{275}{18} \approx 15.28 \text{ m/s} \]

### Step 4: Use the formula for time
The formula for time taken to cover a distance is:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
Substituting the values we have:
\[ \text{Time} = \frac{550 \text{ meters}}{15.28 \text{ m/s}} \]

### Step 5: Calculate the time
Now, calculating the time:
\[ \text{Time} = \frac{550}{15.28} \approx 36 \text{ seconds} \]

### Conclusion
The train will take approximately **36 seconds** to pass the signal post.

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