A train 700 m long is running at the speed of 72 km/h. If it crosses a tunnel in 1 min, then the length of the tunnel (in m) is

Options

A. 500
B. 525
C. 515
D. 505

Answer

To solve the problem of finding the length of the tunnel that a train crosses, we can break it down into a series of steps:

### Step 1: Convert the speed of the train from km/h to m/s
The speed of the train is given as 72 km/h. We need to convert this to meters per second (m/s) using the conversion factor:
1 km/h = (5/18) m/s.

\[ \text{Speed in m/s} = 72 \times \frac{5}{18} = 20 \text{ m/s} \]

### Step 2: Determine the time taken to cross the tunnel in seconds
The time taken to cross the tunnel is given as 1 minute. We need to convert this into seconds.

\[ \text{Time in seconds} = 1 \text{ minute} = 60 \text{ seconds} \]

### Step 3: Calculate the total distance traveled by the train while crossing the tunnel
The total distance traveled by the train while crossing the tunnel can be calculated using the formula:

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

Substituting the values we have:

\[ \text{Distance} = 20 \text{ m/s} \times 60 \text{ s} = 1200 \text{ meters} \]

### Step 4: Determine the length of the tunnel
The total distance traveled by the train while crossing the tunnel is equal to the length of the train plus the length of the tunnel.

Let \( x \) be the length of the tunnel. The length of the train is given as 700 meters. Therefore, we can set up the equation:

\[ \text{Total Distance} = \text{Length of Train} + \text{Length of Tunnel} \]

\[ 1200 = 700 + x \]

### Step 5: Solve for the length of the tunnel
Now, we can solve for \( x \):

\[ x = 1200 - 700 = 500 \text{ meters} \]

### Conclusion
The length of the tunnel is 500 meters.

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