Let’s analyze the problem step-by-step using relative speeds and distances.

1. Define the meeting point and direction of travel:

   • Trains A and B start traveling toward each other from stations X and Y, respectively.
   • They meet at a certain point between X and Y.

2. Information provided:

   • Train A takes 10 minutes to cover the entire distance from X to Y.
   • After meeting Train A, Train B takes 9 more minutes to reach station X.

3. Relative speeds and time:

   • Let the distance between X and Y be $D$.
   • Since Train A covers the distance $D$ in 10 minutes, the speed of Train A is $\frac{D}{10}$.
   • After the trains meet, Train B takes 9 minutes to cover the remaining distance to station X. Let the distance from the meeting point to station X be $d$.

4. Set up equations for distance and time:

   • Since Train B covers distance $d$ in 9 minutes, the speed of Train B is $\frac{d}{9}$.
   • Because they started at the same time and traveled toward each other, their travel times are equal up to the point where they meet.

5. Total time for Train B from Y to X:

   • Since Train A takes 10 minutes to travel from X to Y, the time for Train B to travel from Y to X must also be 10 minutes.

So, the total time taken by Train B to travel from station Y to station X is 10 minutes.

Would you like a detailed breakdown of any step?

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Here are five related questions to deepen your understanding:

1. What if Train B took 8 minutes to reach station X after meeting Train A?
2. How would the answer change if Train A reached station Y in 12 minutes instead of 10?
3. Can you calculate the exact meeting point between stations X and Y?
4. What is the impact of different train speeds on the meeting point?
5. How would this change if both trains had the same speed?

Tip: When solving problems with two moving objects meeting, using relative speeds often simplifies the calculations.