A train 140 m long us running at 60 km per hour . In how much time will it pass a tunnel 260 m long ?

Answer

To solve the problem of how much time a train 140 m long running at 60 km/h will take to pass through a tunnel 260 m long, we can follow these steps:

### Step-by-Step Solution:

1. **Calculate the Total Distance**:
- The total distance that the train needs to cover to completely pass through the tunnel is the sum of the lengths of the train and the tunnel.
- Length of the train = 140 m
- Length of the tunnel = 260 m
- Total distance = Length of the train + Length of the tunnel
- Total distance = 140 m + 260 m = 400 m

**Hint**: Remember that the train must clear both its own length and the length of the tunnel.

2. **Convert Speed from km/h to m/s**:
- The speed of the train is given as 60 km/h. We need to convert this speed into meters per second (m/s).
- Conversion formula:
\[ \text{Speed in m/s} = \text{Speed in km/h} \times \frac{1000 \text{ m}}{1 \text{ km}} \times \frac{1 \text{ h}}{3600 \text{ s}} \]
- So,
\[ \text{Speed} = 60 \times \frac{1000}{3600} = \frac{60000}{3600} = \frac{50}{3} \text{ m/s} \]

**Hint**: To convert km/h to m/s, multiply by \( \frac{5}{18} \).

3. **Calculate Time Taken to Pass the Tunnel**:
- We use the formula for time, which is:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
- Here, the distance is 400 m and the speed is \( \frac{50}{3} \) m/s.
- So,
\[ \text{Time} = \frac{400}{\frac{50}{3}} = 400 \times \frac{3}{50} = \frac{1200}{50} = 24 \text{ seconds} \]

**Hint**: When dividing by a fraction, multiply by its reciprocal.

### Final Answer:
The train will take **24 seconds** to pass through the tunnel.