A train moves at a speed of 35 m/sec and crosses a tunnel of length 960 metres, in 40 seconds. What is the length (in metres) of the train?

Options

A. 360
B. 440
C. 530
D. 560

Answer

To find the length of the train, we can follow these steps:

### Step 1: Understand the problem
We know the speed of the train, the length of the tunnel, and the time taken to cross the tunnel. We need to find the length of the train.

### Step 2: Write down the known values
- Speed of the train (S) = 35 m/sec
- Length of the tunnel (L_tunnel) = 960 m
- Time taken to cross the tunnel (T) = 40 sec

### Step 3: Calculate the total distance traveled by the train
The total distance (D) traveled by the train while crossing the tunnel can be calculated using the formula:
\[ D = S \times T \]
Substituting the known values:
\[ D = 35 \, \text{m/sec} \times 40 \, \text{sec} \]
\[ D = 1400 \, \text{m} \]

### Step 4: Set up the equation for the total distance
The total distance traveled by the train while crossing the tunnel is equal to the length of the tunnel plus the length of the train (let's denote the length of the train as \( x \)):
\[ D = L_tunnel + x \]
Substituting the values we have:
\[ 1400 = 960 + x \]

### Step 5: Solve for the length of the train
To find \( x \), we rearrange the equation:
\[ x = 1400 - 960 \]
\[ x = 440 \, \text{m} \]

### Conclusion
The length of the train is **440 meters**.

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