Is your 11:15 flight to PHL with US Air?
If so, you will need to go to T5, while the train station is across from T3. There is a shuttle bus that connects the two (I suggest you don't walk to it) every 10 to 15 min. Between walking from the train station to T3 and the shuttle bus transfer you could waste an additional 20-25 min.
So you will have less than 1 hour until the flight departure.
In order to make the flight you need to be at the gate 15 min prior to departure which is when the flight closes.
Will 30-40 minutes be enough to complete the following steps?
- Stand in line at the check in counter at T5 to check in.
- Go through the security line and passport control at T5
- Wait for the shuttle bus airside which will take you back to T3 where the flight actually departs from.
- Take the people mover from T3 to the T3 satellite terminal where flights to North America depart from.
- Board.
I don't know the answer to that question, but I think it would be cutting it very close.
You could do this if it was a EU Schengen flight, which goes to a European hub first, but with an intercontinental flight to North America operated by a US airline (i.e. with check in at T5) I wouldn't chance it.
I would leave for Rome the day before and spend the last night in Rome. Actually that is what I always do when I depart from Rome (and I also come from Florence).