A 120 m long train is moving in a direction with speed 20 m/s . A traing B moving with 30 m/s in the opposite direction and 130 m long crosses the first train in a time

Options

A. 6s
B. 36 s
C. 38 s
D. none of these

Explanation

To solve the problem, we need to find the time it takes for Train B to completely cross Train A. Here’s a step-by-step breakdown of the solution:

### Step 1: Identify the lengths of the trains
- Length of Train A = 120 m
- Length of Train B = 130 m

### Step 2: Calculate the total distance to be covered
When Train B crosses Train A, it needs to cover the entire length of both trains. Therefore, the total distance \( D \) is:
\[ D = \text{Length of Train A} + \text{Length of Train B} = 120 \, \text{m} + 130 \, \text{m} = 250 \, \text{m} \]

### Step 3: Determine the speeds of the trains
- Speed of Train A = 20 m/s (moving in one direction)
- Speed of Train B = 30 m/s (moving in the opposite direction)

### Step 4: Calculate the relative velocity
Since the trains are moving towards each other, we can add their speeds to find the relative velocity \( V_{rel} \):
\[ V_{rel} = \text{Speed of Train A} + \text{Speed of Train B} = 20 \, \text{m/s} + 30 \, \text{m/s} = 50 \, \text{m/s} \]

### Step 5: Calculate the time taken to cross
The time \( t \) taken for Train B to cross Train A can be calculated using the formula:
\[ t = \frac{D}{V_{rel}} = \frac{250 \, \text{m}}{50 \, \text{m/s}} = 5 \, \text{s} \]

### Conclusion
The time taken for Train B to completely cross Train A is **5 seconds**.

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