A `150 m` long train is moving with a uniform velocity of `45 km//h`. The time taken by the train to cross a bridge of length `850` metres is.

Options

A. 56 sec
B. 68 sec
C. 80 sec
D. 92 sec

Explanation

To solve the problem of how long it takes for a train to cross a bridge, we can break it down into clear steps:

### Step 1: Understand the Problem
We have a train that is 150 meters long and is moving at a speed of 45 km/h. We need to find out how long it takes for this train to completely cross a bridge that is 850 meters long.

### Step 2: Convert Speed to Meters per Second
The speed of the train is given in kilometers per hour (km/h), and we need to convert it to meters per second (m/s) for consistency with the distance units.

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

Substituting the given speed:

\[ \text{Speed} = 45 \times \frac{5}{18} = 12.5 \text{ m/s} \]

### Step 3: Calculate the Total Distance to be Covered
To find the total distance the train needs to cover to completely cross the bridge, we need to add the length of the train to the length of the bridge.

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

Substituting the values:

\[ \text{Total Distance} = 850 \text{ m} + 150 \text{ m} = 1000 \text{ m} \]

### Step 4: Calculate the Time Taken to Cross the Bridge
Now we can use the formula for time, which is:

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

Substituting the total distance and speed:

\[ \text{Time} = \frac{1000 \text{ m}}{12.5 \text{ m/s}} = 80 \text{ seconds} \]

### Conclusion
The time taken by the train to cross the bridge is **80 seconds**.

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