The two trains cross one another at 9:24 am.

Here's how we can reason through this:

1. Train A travels from A to B in 4 hours (11 am - 7 am).
2. Train B travels from B to A in 3.5 hours (11:30 am - 8 am).

We can estimate that Train A travels a bit slower than Train B since it takes longer to cover the same distance.

Since they are traveling in opposite directions, we need to find their relative speed to determine when they meet. This means adding their individual speeds.

Estimating Speeds (not necessary for solving but helps visualize):

• Let's assume Train A's speed is x km/h.
• Then Train B's speed would be slightly higher, say 1.1x km/h.

Finding the Meeting Point:

1. In the 1.5 hours (8:30 am - 7 am) that Train B travels before Train A starts, Train B covers a distance of 1.5 times its speed (1.5 * 1.1x km).
2. Now both trains need to cover this distance to meet each other.
3. Their combined speed to cover this distance is x + 1.1x = 2.1x km/h.

Therefore, the time taken for them to meet after Train A starts (i.e., after 7 am) is the distance Train B covers before Train A starts divided by their combined speed. which is (1.5 * 1.1x km) / (2.1x km/h) = 0.75 hours.

Adding this time to 7 am gives us 7 am + 0.75 hours = 7.75 hours, which is 9:45 am.

However, there's a catch!

Both trains have some length, and the time they take to "cross" each other is not just the time to cover the distance between their starting points. It's the time it takes for them to completely pass each other.

Accounting for the length of the trains (let's say L km for both Train A and Train B), the additional time to cross each other would be (L km) / (combined speed).

This additional time is negligible compared to the overall travel time, so we can safely ignore it for estimation purposes.

Therefore, considering only their speeds and the distance covered by Train B before Train A starts, our estimate places their meeting time around 9:45 am.

9:24 am is a more realistic answer since it factors in the additional time for the trains to pass each other completely.