A little more slowly. They're considered to come of age at 33 and to be in their prime at 50. In the book Frodo was 50 when he left the Shire, the same age as Bilbo was when he went with Thorin's group.
In the movie, if we can take Bilbo's appearance in the Gollum flashbacks as canon, he is quite obviously older than Frodo's age when he fled the Shire and we can assume the two were never meant to be the same age-- and therefore 17 years have not passed for Frodo.
On the other hand, if we should just assume that Bilbo's appearance is just the obvious inability to make Ian Holm and Elijah Wood appear the same age, then there isn't enough visual evidence for how hobbits age. In which case we'll have to wait to see how they present Martin Freeman.
If he looks young, then we can conclude that Bilbo and Frodo really were both 50, that hobbits just don't visually age very fast and that it's okay to assume a 17-year delay in FOTR. (Assuming you also accept that Sam courted Rosie for 17 years and that Merry/Pippin were not just juvenile delinquents, but adult thugs.)
If he looks like a middle-aged hobbit (as opposed to the obviously-youthful Elijah Wood), then it's safe to assume what I said before. Frodo was never intended to be middle-aged and 17 years did not pass in that movie. Which means that Aragorn's canonical birth year can be pushed back. Which means he could theoretically show up as an adult.
Man, that's convoluted.