A train of length 150m takes 40.5 seconds to cross a tunnel of length 300m. The speed of the train (in km/hr) is

Options

A. 40
B. `26(2)/(3)`
C. `13(1)/(3)`
D. 48

Answer

To find the speed of the train in kilometers per hour, we can follow these steps:

### Step 1: Calculate the total distance
The total distance that the train travels while crossing the tunnel is the sum of the length of the train and the length of the tunnel.

- Length of the train = 150 meters
- Length of the tunnel = 300 meters

**Total distance = Length of the train + Length of the tunnel**
\[ \text{Total distance} = 150 \, \text{m} + 300 \, \text{m} = 450 \, \text{m} \]

### Step 2: Identify the total time taken
The total time taken for the train to cross the tunnel is given as 40.5 seconds.

### Step 3: Use the speed formula
The formula for speed is:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]

Substituting the values we have:
\[ \text{Speed} = \frac{450 \, \text{m}}{40.5 \, \text{s}} \]

### Step 4: Calculate the speed in meters per second
Now, we will perform the division:
\[ \text{Speed} = \frac{450}{40.5} \approx 11.11 \, \text{m/s} \]

### Step 5: Convert speed to kilometers per hour
To convert the speed from meters per second to kilometers per hour, we use the conversion factor \( \frac{18}{5} \):
\[ \text{Speed in km/hr} = 11.11 \, \text{m/s} \times \frac{18}{5} \]

Calculating this gives:
\[ \text{Speed in km/hr} = 11.11 \times 3.6 \approx 40 \, \text{km/hr} \]

### Final Answer
The speed of the train is **40 km/hr**.

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