What's the shortest amount of time someone has ever learned a new language while living among it day in and day out for x amount of time? A (secondary) character is going to be living among this society he's new to for a while, but he doesn't speak their language. However, he'll be interacting with them quite a bit while he's there (my main character speaks both languages fine, so translation isn't an issue), and I'd like him to learn it as quickly as possible (and he wants to as well I might add). I just wanted to a good idea of what jaw-dropping, "wow fast" would be for learning a foreign language through day-to-day interaction with it, not necessarily by sitting down and having someone TEACH it to him for a couple hours a day.
I could make up a timeframe, but I didn't want it to be completely unbelievable (as opposed to really impressive), as I only know this language, and the only classes I took I was terrible at. If it helps, this character is a very dedicated, fast learner.
Thank you ahead of time!