A porter standing on platform find that a train crosses him in 4 sec. and another train of equal length going in opposite direction crosses him in 5 sec. How much time (in sec.) will they take to cross ?

Options

A. 35
B. 36.5
C. `(40)/(9)`
D. None

Answer

To solve the problem, we need to find the time it takes for two trains of equal length to cross each other when they are moving in opposite directions. We have the time it takes for each train to cross a stationary porter.

### Step-by-step Solution:

1. **Identify the Variables:**
- Let the length of each train be \( L \).
- Let the speed of the first train be \( S_1 \).
- Let the speed of the second train be \( S_2 \).

2. **Calculate the Speed of Each Train:**
- The first train crosses the porter in 4 seconds, so:
\[ S_1 = \frac{L}{4} \]
- The second train crosses the porter in 5 seconds, so:
\[ S_2 = \frac{L}{5} \]

3. **Calculate the Relative Speed:**
- When two trains are moving in opposite directions, their relative speed is the sum of their speeds:
\[ S_{relative} = S_1 + S_2 = \frac{L}{4} + \frac{L}{5} \]
- To add these fractions, we need a common denominator. The least common multiple of 4 and 5 is 20:
\[ S_{relative} = \frac{5L}{20} + \frac{4L}{20} = \frac{9L}{20} \]

4. **Calculate the Time to Cross Each Other:**
- The total distance to be covered when the two trains cross each other is the sum of their lengths, which is \( L + L = 2L \).
- The time taken to cross each other is given by:
\[ \text{Time} = \frac{\text{Total Distance}}{\text{Relative Speed}} = \frac{2L}{\frac{9L}{20}} = 2L \times \frac{20}{9L} = \frac{40}{9} \]
- This simplifies to approximately \( 4.44 \) seconds.

### Final Answer:
The time taken for the two trains to cross each other is approximately \( 4.44 \) seconds.