A 100 m long train is moving with a uniform velocity of `45 km//hr`. The time taken by the train to cross a bridge of length 1 km is

Options

A. 58s
B. 68s
C. 8s
D. 88s

Answer

To solve the problem of how long it takes for a 100 m long train moving at a uniform velocity of 45 km/h to cross a bridge of length 1 km, we can follow these steps:

### Step-by-Step Solution:

1. **Convert the Length of the Bridge to Meters**:
- The length of the bridge is given as 1 km.
- Convert this to meters:
\[ 1 \text{ km} = 1000 \text{ m} \]

2. **Calculate the Total Distance to be Covered**:
- The train must cover its own length plus the length of the bridge to completely cross it.
- The length of the train is 100 m, and the length of the bridge is 1000 m.
- Therefore, the total distance \( D \) is:
\[ D = \text{Length of Train} + \text{Length of Bridge} = 100 \text{ m} + 1000 \text{ m} = 1100 \text{ m} \]

3. **Convert the Speed from km/h to m/s**:
- The speed of the train is given as 45 km/h.
- To convert this to meters per second, use the conversion factor \( \frac{5}{18} \):
\[ \text{Speed} = 45 \text{ km/h} \times \frac{5}{18} = 12.5 \text{ m/s} \]

4. **Calculate the Time Taken to Cross the Bridge**:
- Use the formula for time, which is:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
- Substitute the values:
\[ \text{Time} = \frac{1100 \text{ m}}{12.5 \text{ m/s}} = 88 \text{ seconds} \]

### Final Answer:
The time taken by the train to cross the bridge is **88 seconds**.

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