A train 350 m long is runing at the speed of 36 km/h if it crosses a tunnel in 1 minute the the length of the tunnel ( in metres ) is:

Options

A. 200 m
B. 250 m
C. 150 m
D. none of these

Answer

To solve the problem of finding the length of the tunnel that a train crosses in 1 minute, we can follow these steps:

### Step 1: Understand the problem
We have a train that is 350 meters long and is moving at a speed of 36 km/h. It crosses a tunnel in 1 minute, and we need to find the length of the tunnel.

### Step 2: Convert the speed from km/h to m/s
To convert the speed from kilometers per hour (km/h) to meters per second (m/s), we use the conversion factor:
\[ 1 \text{ km/h} = \frac{1000 \text{ meters}}{3600 \text{ seconds}} \]
So, we convert 36 km/h:
\[ 36 \text{ km/h} = 36 \times \frac{1000}{3600} = 10 \text{ m/s} \]

### Step 3: Convert the time from minutes to seconds
The time given is 1 minute. We convert this to seconds:
\[ 1 \text{ minute} = 60 \text{ seconds} \]

### Step 4: Calculate the total distance traveled by the train
The distance traveled by the train in 1 minute (60 seconds) can be calculated using the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
Substituting the values we have:
\[ \text{Distance} = 10 \text{ m/s} \times 60 \text{ seconds} = 600 \text{ meters} \]

### Step 5: Set up the equation for the total distance
The total distance covered by the train while crossing the tunnel is equal to the length of the train plus the length of the tunnel (let's denote the length of the tunnel as \( X \)):
\[ \text{Total Distance} = \text{Length of Train} + \text{Length of Tunnel} \]
This can be expressed as:
\[ 600 = 350 + X \]

### Step 6: Solve for the length of the tunnel
Now, we can solve for \( X \):
\[ X = 600 - 350 = 250 \text{ meters} \]

### Final Answer
The length of the tunnel is **250 meters**.

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