We received a question by email I am posting with my answer here, so that it can be useful to anyone on the forum.

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Samantha asks:
How much does it cost to travel by train from Rome to Florence?

The cost of the ticket from Rome to Florence goes from 15 euros in second class on a Regional train (don't recommend it as it stops too many times) to 52 euros for the fastest train traveling in first class (32 euros in second class on this faster train). The difference between first and second class is relative - usually nicer seats, less crowded wagons in first class. If you plan to travel by train, you can try both classes on different legs of your trip to see which ones you prefer. You can buy some tickets online but it is also convenient to wait and buy them in the station when you need them.

You can check out schedules and fares at Trenitalia - Ferrovie dello Stato