Two trains of equal length, running in opposite directions, pass a pole in 18 and 12 seconds. The trains will cross each other in

Options

A. 14.4 seconds
B. 15.5 seconds
C. 18.8 seconds
D. 20.2 seconds

Answer

To solve the problem of two trains of equal length passing each other, we can follow these steps:

### Step 1: Define Variables
Let the length of each train be \( X \) meters.

### Step 2: Calculate Speeds
- The speed of the first train can be calculated as:
\[ \text{Speed of first train} = \frac{X}{18} \text{ meters per second} \]
- The speed of the second train can be calculated as:
\[ \text{Speed of second train} = \frac{X}{12} \text{ meters per second} \]

### Step 3: Determine Total Distance to be Covered
When the two trains cross each other, they need to cover a distance equal to the sum of their lengths. Therefore, the total distance \( D \) is:
\[ D = X + X = 2X \text{ meters} \]

### Step 4: Calculate Combined Speed
Since the trains are moving in opposite directions, their speeds will add up:
\[ \text{Combined speed} = \frac{X}{18} + \frac{X}{12} \]

To add these fractions, we need a common denominator. The least common multiple of 18 and 12 is 36. Thus, we convert the speeds:
\[ \frac{X}{18} = \frac{2X}{36}, \quad \frac{X}{12} = \frac{3X}{36} \]
Now, adding these gives:
\[ \text{Combined speed} = \frac{2X}{36} + \frac{3X}{36} = \frac{5X}{36} \text{ meters per second} \]

### Step 5: Calculate Time to Cross Each Other
The time \( T \) taken to cross each other can be calculated using the formula:
\[ T = \frac{\text{Distance}}{\text{Speed}} = \frac{2X}{\frac{5X}{36}} = 2X \cdot \frac{36}{5X} \]
The \( X \) cancels out:
\[ T = \frac{72}{5} \text{ seconds} \]

### Step 6: Convert to Decimal
Calculating \( \frac{72}{5} \):
\[ T = 14.4 \text{ seconds} \]

### Conclusion
The two trains will cross each other in **14.4 seconds**.

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