A train 800 metres long is running at the speed of 78 km/hr. If it crosses a tunnel in 1 minute, then the length of the tunnel (in metres) is :

Options

A. 77200
B. 500
C. 1300
D. 13

Answer

To solve the problem of finding the length of the tunnel that a train crosses in one minute, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given data:**
- Length of the train = 800 meters
- Speed of the train = 78 km/hr
- Time taken to cross the tunnel = 1 minute

2. **Convert the speed from km/hr to m/s:**
- To convert km/hr to m/s, we use the conversion factor \( \frac{5}{18} \).
- Speed in m/s = \( 78 \times \frac{5}{18} \)
- Speed in m/s = \( \frac{390}{18} = 21.67 \) m/s (approximately)

3. **Convert the time from minutes to seconds:**
- Time = 1 minute = 60 seconds

4. **Calculate the distance traveled by the train in 1 minute:**
- Distance = Speed × Time
- Distance = \( 21.67 \, \text{m/s} \times 60 \, \text{s} \)
- Distance = \( 1300 \, \text{meters} \)

5. **Set up the equation for the total distance:**
- When the train crosses the tunnel, it covers its own length plus the length of the tunnel.
- Total distance = Length of the train + Length of the tunnel
- \( 1300 = 800 + \text{Length of the tunnel} \)

6. **Solve for the length of the tunnel:**
- Length of the tunnel = \( 1300 - 800 \)
- Length of the tunnel = \( 500 \, \text{meters} \)

### Final Answer:
The length of the tunnel is **500 meters**.

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