Let’s break down the problem step by step.

1. Let $T$ be the time at which Trains A and B meet each other after starting their journeys towards each other.

2. Train A reaches station Y in 10 minutes after starting from station X. Therefore, it takes Train A 10 minutes to cover the entire distance between stations X and Y.

3. Train B takes 9 minutes to reach station X after meeting Train A.

Since both trains started at the same time and traveled at constant speeds, the ratio of their speeds will be the inverse of the ratio of their times to cover the full distance.

The total travel time for Train B from station Y to station X can be calculated as follows:

Since Train A takes 10 minutes to travel from X to Y, the distance ratio covered by Train A and Train B by the time they meet can be used to find the total time for Train B’s journey:

Let: $\text{Total time for Train B} = 10 + 9 = 19 \text{ minutes}$

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

Would you like further details or have any questions?

Related Questions

1. How would the answer change if Train A took 15 minutes to reach station Y?
2. What if Train B took only 6 minutes to reach station X after meeting Train A?
3. How do you calculate the relative speed between two objects moving towards each other?
4. How would the meeting time $T$ be affected if Train B traveled faster than Train A?
5. How can we use the concept of speed ratios to solve similar problems?

Tip:

In problems involving two moving objects meeting, understanding the ratio of their speeds and distances is key to simplifying calculations.