train leaves statlon A at 5 AM and reaches sta-. 
.tion B at 9 AM. on the same day. Anothër traln 
leaves station B at 7 AM and reaches statlon A at 
10:30 AM on the same day. The time at whlch the 
two trains cross each other ls :

Let's define the problem step by step.

1. **Train A** leaves **Station A** at 5 AM and reaches **Station B** at 9 AM. Therefore, the total travel time for Train A is:
   \[
   9 \, \text{AM} - 5 \, \text{AM} = 4 \, \text{hours}.
   \]

2. **Train B** leaves **Station B** at 7 AM and reaches **Station A** at 10:30 AM. The total travel time for Train B is:
   \[
   10:30 \, \text{AM} - 7 \, \text{AM} = 3.5 \, \text{hours}.
   \]

Now, let's assume the two trains meet at some point after Train A leaves at 5 AM, but before Train B arrives at Station A.

### Step 1: Distance Proportions
Assuming that both trains travel at constant speeds, we know that when they meet, the distance each train has traveled is proportional to the time they have spent traveling.

Let **\( t \)** represent the time (in hours) after **7 AM** when they meet.

- **Train A** starts at 5 AM, so by the time Train B leaves at 7 AM, Train A has already been traveling for 2 hours.
- The two trains will meet at some point **\( t \)** hours after 7 AM.

Thus, by the time they meet, Train A has been traveling for:
\[
2 + t \, \text{hours}.
\]

Train B has been traveling for:
\[
t \, \text{hours}.
\]

### Step 2: Speed Ratios
The total time taken by Train A and Train B are 4 hours and 3.5 hours, respectively. This gives the speed ratio of the two trains as:
\[
\text{Speed of Train A} : \text{Speed of Train B} = 3.5 \, \text{hours} : 4 \, \text{hours} = 7:8.
\]
Thus, for every 8 units of distance Train A covers, Train B covers 7 units in the same amount of time.

### Step 3: Meeting Point
At the meeting point, the distance covered by Train A is proportional to 8 units, and the distance covered by Train B is proportional to 7 units.

Thus, the combined time before they meet is proportional to:
\[
(2 + t) \times \frac{7}{8} = t
\]

This equation represents the balance of distances each has covered by the

Train leaves station A at 5 AM and reaches station B at 9 AM. Another train leaves station B at 7 AM and reaches station A at 10:30 AM. The time at which the two trains cross each other is:

Solve the problem of finding when two trains cross each other between Station A and Station B. The solution covers proportionality, speed ratios, and time-distance relationships, suitable for students in Grades 9-10.

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