A "week" in travel time actually last longer than 7 days
This is a less obvious question than it might sound. There are actually nine days in a travel week.
In terms of a European vacation, the Beatles were off by only one day.
- One week lasts 9 days
- Two weeks last 17 days
The itineraries assume you're catching an overnight flight on Friday (even if you have to leave work a bit early) and are flying back on the Sunday right before you have to return to work.
This means you land in Rome on a Saturday morning, and although you'll spend much of that morning getting through customs, collecting your bags, getting downtown from the airport, and settling into your hotel, it's still the first day of your trip.
(Accordingly, these itineraries all assume your first day consists only of the afternoon—and that you'll be jet-lagged and ready to turn in early that evening.)
The following Saturday is your eighth day in Europe and the final full day of being a tourist. That last Sunday is pretty much spent just getting up, getting to the airport, and getting home.
Add it that up, and you get a total of nine days.
A note about that final Sunday
Most flights back to North America leave Europe either in the morning or, at the latest, around 3pm.
Either way—considering you have to leave for the airport four hours early, once you figure on one hour for transit, two hours for check-in regulations, and one more hour as a cushion for unforeseen delays/long lines—you end up spending all of that final Sunday simply getting to the airport and flying home.
It's still part of your trip, but doesn't really count as a day of vacation; it's sheer transportation.
Consider it the bonus day of your trip: at least you still get to have one last cappuccino and cornetto, even if it is at the airport bar.