A 153 m Iong train crosses a 747 m long bridge in 40.5 seconds. "What is the speed of the train?

Options

A. 80 km/h
B. 70 km/h
C. 75 km/h
D. 85 km/h

Answer

To solve the problem of finding the speed of the train that crosses a bridge, we can follow these steps:

### Step 1: Identify the lengths involved
- Length of the train = 153 meters
- Length of the bridge = 747 meters

### Step 2: Calculate the total distance to be covered
To find the total distance the train needs to cover while crossing the bridge, we add the length of the train and the length of the bridge together.

\[ \text{Total Distance} = \text{Length of Train} + \text{Length of Bridge} \]
\[ \text{Total Distance} = 153 \, \text{m} + 747 \, \text{m} = 900 \, \text{m} \]

### Step 3: Identify the time taken to cross the bridge
The time taken for the train to cross the bridge is given as 40.5 seconds.

### Step 4: Use the formula for speed
Speed is calculated using the formula:

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

Substituting the values we have:

\[ \text{Speed} = \frac{900 \, \text{m}}{40.5 \, \text{s}} \]

### Step 5: Calculate the speed in meters per second
Now, we perform the division:

\[ \text{Speed} = \frac{900}{40.5} \approx 22.22 \, \text{m/s} \]

### Step 6: Convert speed to kilometers per hour
To convert the speed from meters per second to kilometers per hour, we use the conversion factor \( \frac{18}{5} \):

\[ \text{Speed in km/h} = \text{Speed in m/s} \times \frac{18}{5} \]
\[ \text{Speed in km/h} = 22.22 \, \text{m/s} \times \frac{18}{5} \approx 80 \, \text{km/h} \]

### Final Answer
The speed of the train is approximately **80 kilometers per hour**.

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