The metro service has a train going from A to B and B to A every hour, the first one at 6 a.m. The trip from one city to other takes 4.5 hours, and all trains travel at the same speed. How many trains will you pass while going from A to B if you start at 12 noon?

Answer

To solve the problem, we need to determine how many trains you will pass while traveling from A to B if you start at 12 noon.

### Step-by-Step Solution:

1. **Understand the Train Schedule**:
- Trains leave from A to B and B to A every hour starting from 6 a.m.
- The first train from A to B leaves at 6 a.m., and the last one before noon leaves at 12 p.m.

2. **Calculate the Duration of the Journey**:
- The journey from A to B takes 4.5 hours.

3. **Determine the Time Frame**:
- If you start your journey at 12 noon, you will arrive at B at 4:30 p.m. (12:00 p.m. + 4.5 hours).

4. **Identify the Trains Departing from A to B**:
- The trains from A to B that will be on the track during your journey from 12:00 p.m. to 4:30 p.m. are those that left A at 6 a.m., 7 a.m., 8 a.m., 9 a.m., 10 a.m., 11 a.m., 12 p.m., and 1 p.m.
- The train that left at 1 p.m. will still be on its way to B when you start your journey.

5. **Count the Trains from A to B**:
- The trains that left A before you start your journey are:
- 6 a.m. (arrives at 10:30 a.m.)
- 7 a.m. (arrives at 11:30 a.m.)
- 8 a.m. (arrives at 12:30 p.m.)
- 9 a.m. (arrives at 1:30 p.m.)
- 10 a.m. (arrives at 2:30 p.m.)
- 11 a.m. (arrives at 3:30 p.m.)
- 12 p.m. (arrives at 4:30 p.m.)
- 1 p.m. (arrives at 5:30 p.m.)
- This gives us a total of **8 trains** that you will pass going from A to B.

6. **Identify the Trains Departing from B to A**:
- Trains leave from B to A every hour starting from 6 a.m.
- The trains that will be on the track while you are traveling are those that left B at 6 a.m., 7 a.m., 8 a.m., 9 a.m., 10 a.m., 11 a.m., 12 p.m., 1 p.m., 2 p.m., 3 p.m., and 4 p.m.
- The trains that left B at 6 a.m. to 11 a.m. will still be on the track until you reach B at 4:30 p.m.
- This gives us a total of **11 trains** that you will pass coming from B to A.

### Total Trains Passed:
- **Total Trains Passed = Trains from A to B + Trains from B to A = 8 + 11 = 19 trains.**

### Final Answer:
You will pass a total of **19 trains** while going from A to B if you start at 12 noon.