Two trains are each 50 m long moving parallel towards each other at speeds `10 ms^(-1)` and `15 ms^(-1)` respectively, at what time will they pass each other ?

Options

A. 8 s
B. 4 s
C. 2 s
D. 6 s

Explanation

To solve the problem of when the two trains pass each other, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Length of the Trains**:
Each train is 50 meters long. Therefore, the total length that needs to be covered for the trains to completely pass each other is:
\[ \text{Total Length} = 50 \, \text{m} + 50 \, \text{m} = 100 \, \text{m} \]

2. **Determine the Speeds of the Trains**:
The speeds of the two trains are given as:
- Train A: \(10 \, \text{ms}^{-1}\)
- Train B: \(15 \, \text{ms}^{-1}\)

3. **Calculate the Relative Speed**:
Since the trains are moving towards each other, we can find the relative speed by adding their speeds:
\[ \text{Relative Speed} = 10 \, \text{ms}^{-1} + 15 \, \text{ms}^{-1} = 25 \, \text{ms}^{-1} \]

4. **Calculate the Time to Pass Each Other**:
To find the time taken for the trains to completely pass each other, we use the formula:
\[ \text{Time} = \frac{\text{Total Length}}{\text{Relative Speed}} = \frac{100 \, \text{m}}{25 \, \text{ms}^{-1}} = 4 \, \text{s} \]

### Final Answer:
The time taken for the two trains to pass each other is **4 seconds**.

---