A 100 m long train crosses a 800 m long bridge. If the speed of train 30 km/h, then what is the time taken to cross the bridge ?

Options

A. 105 s
B. 108 s
C. 118 s
D. 120 s

Answer

To solve the problem of how long it takes for a 100 m long train traveling at a speed of 30 km/h to cross an 800 m long bridge, we can follow these steps:

### Step 1: Convert the speed from km/h to m/s
The speed of the train is given as 30 km/h. We need to convert this to meters per second (m/s) using the conversion factor:
\[ 1 \text{ km/h} = \frac{5}{18} \text{ m/s} \]

So,
\[ 30 \text{ km/h} = 30 \times \frac{5}{18} \text{ m/s} = \frac{150}{18} \text{ m/s} = \frac{25}{3} \text{ m/s} \]

### Step 2: Calculate the total distance to be covered
The total distance the train needs to cover to completely cross the bridge is the sum of the length of the train and the length of the bridge:
\[ \text{Total Distance} = \text{Length of Train} + \text{Length of Bridge} = 100 \text{ m} + 800 \text{ m} = 900 \text{ m} \]

### Step 3: Use the formula to calculate time
We can use the formula for time, which is derived from the relationship between speed, distance, and time:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

Substituting the values we have:
\[ \text{Time} = \frac{900 \text{ m}}{\frac{25}{3} \text{ m/s}} \]

### Step 4: Simplify the calculation
To simplify this division, we can multiply by the reciprocal:
\[ \text{Time} = 900 \text{ m} \times \frac{3}{25} = \frac{2700}{25} \text{ seconds} \]

Calculating \( \frac{2700}{25} \):
\[ \text{Time} = 108 \text{ seconds} \]

### Final Answer
The time taken for the train to cross the bridge is **108 seconds**.

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