Train A and B stars travelling at the same speed towards each other with constant speed from stations X and Y, respectively. Train A reaches station Y in 10 minutes and B reaches station X in 9 minutes after meeting each other. Total time taken by B to reach from Station X to Y is..?

Let's denote the distance between stations \( X \) and \( Y \) as \( D \). Let the speed of Train A be \( v_A \) and the speed of Train B be \( v_B \). 

### Step 1: Understanding the problem

- Train A takes 10 minutes to reach station \( Y \) after meeting Train B.
- Train B takes 9 minutes to reach station \( X \) after meeting Train A.
- Both trains are traveling towards each other and meet at a point between stations \( X \) and \( Y \).
- The total time taken by Train B to travel from station \( X \) to station \( Y \) is what we need to find.

### Step 2: Establish relationships between distances and speeds

When the trains meet:
- The remaining distance for Train A to reach station \( Y \) is \( v_A \times 10 \) (since \( v_A \) is the speed and \( 10 \) minutes is the time).
- The remaining distance for Train B to reach station \( X \) is \( v_B \times 9 \).

Since the total distance \( D \) is covered by both trains together:
- \( D = v_A \times 10 + v_B \times 9 \).

### Step 3: Find the relationship between \( v_A \) and \( v_B \)

The time taken by Train A and Train B to reach the meeting point from their respective starting points must be equal because they meet at the same time. Let the time taken to meet be \( t \) minutes.

- For Train A: \( \text{Distance} = v_A \times t \)
- For Train B: \( \text{Distance} = v_B \times t \)

Since \( v_A = v_B \) (they have the same speed), the distance traveled by both trains before meeting will also be the same.

### Step 4: Find the time for Train B to travel from \( X \) to \( Y \)

We need to find the total time \( T \) for Train B to travel from \( X \) to \( Y \):
\[ T = t + 9 \text{ minutes} \]

However, since \( v_A = v_B \), \( v_B = v_A \), and the distance \( D \) is the same for both, the time \( t \) is directly proportional to the time it takes Train A to reach after the meeting point:

\[ T = \frac{9 + 10}{2} \times 2 \]

Here, the total time \( T \) is equal to the average of the two times multiplied by 2 (since the trains have the same speed and travel the entire distance):

\[
T = \frac{19}{2} \times 2 = 19 \text{ minutes}
\]

Thus, the total time taken by Train B to travel from station \( X \) to station \( Y \) is **19 minutes**.

Would you like further details or explanations on any part? Here are some additional questions you might consider:

1. How would the answer change if the trains had different speeds?
2. What if the time taken by Train A to reach station \( Y \) was doubled?
3. How would the solution differ if one train stopped halfway?
4. Can you calculate the exact meeting point between stations \( X \) and \( Y \)?
5. What if Train B took a different route that was longer than Train A's route?
6. How does the symmetry of the problem affect the solution?
7. What happens if Train B starts later than Train A?
8. Can this problem be solved using relative speed concepts?

**Tip:** When dealing with problems involving two moving objects, symmetry can simplify your calculations.

Understand how to calculate the total time taken by Train B to travel from station X to station Y when two trains meet and continue towards their destinations. Detailed solution involving speed, distance, and time calculations.

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