The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 second is

Options

A. 200 m
B. 250 m
C. 245 m
D. 250 m

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Identify the given data
- Length of the train (L_train) = 130 meters
- Speed of the train (V) = 45 km/hr
- Time to cross the bridge (t) = 30 seconds

### Step 2: Convert the speed from km/hr to m/s
To convert the speed from kilometers per hour to meters per second, we use the conversion factor:
\[ 1 \text{ km/hr} = \frac{5}{18} \text{ m/s} \]
So,
\[ V = 45 \text{ km/hr} \times \frac{5}{18} = \frac{225}{18} = 12.5 \text{ m/s} \]

### Step 3: Use the formula for speed
The formula for speed is:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
In this case, the distance is the total distance covered by the train while crossing the bridge, which is the length of the train plus the length of the bridge (L_bridge). Therefore, we can write:
\[ V = \frac{L_{\text{train}} + L_{\text{bridge}}}{t} \]

### Step 4: Substitute the known values into the equation
Substituting the known values into the equation:
\[ 12.5 = \frac{130 + x}{30} \]
Where \( x \) is the length of the bridge.

### Step 5: Rearrange the equation to solve for x
Multiply both sides by 30:
\[ 12.5 \times 30 = 130 + x \]
\[ 375 = 130 + x \]

### Step 6: Solve for x
Now, isolate \( x \):
\[ x = 375 - 130 \]
\[ x = 245 \text{ meters} \]

### Conclusion
The length of the bridge is 245 meters.

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