What took the Jews 8 days to produce new oil when rededicating the Temple in the Chanuka story? It seems the process of oil-making takes a lot less time (I have done it in Israel on one of the tourist trips), so what exactly historically took 8 days?
Another answer (Beis Yosef, Orach Chaim 670, s.v. והטעם) is that the actual pressing would indeed take a day, but that they first had to undergo seven days of purification (from tum'ah contracted by contact with corpses, of which there were plenty during the battles against the Syrian-Greeks) - since, after all, the whole point was that they needed oil that was free of tum'ah.
Adding to what @GershonGold brought in the name of the Meiri, Rabbi Dr. Shmuel Klein in his book "Eretz Hagalil" (Land of Galilee), pg. 20-21 writes (my translation):
"One of the Gaonim of Babylon was asked: "Why do we keep eight days of Chanukah...and why do we have eight nights and it didn't last more or less than that?"
Because the oils came from the land of Asher, as it says: "May he dip his foot in oil", and he had a place called Tekoa, as they say: "Tekoa, the primary source of oil" (Mishna Menachot 8:3), that from there the oils come, and from there until Yerushalayim it took eight days to walk to and back...and therefore they waited until pure oil was brought from there, and that is why the miracle lasted for eight days.
This answer is very important, because never do we see anywhere in the Talmud that the length of the road from Yerushalayim to Tekoa back and forth was eight days. So too do we not find anywhere that the oil for the Menorah in the Temple was brought from Tekoa in the land of Asher, and in particular, it is not said that this was so in the time of Chanukah in the days of the Chashmonaim. If, however, the Gaon was able to tell us all of these things, and in accurate detail, we must surely assume that he had by him ancient traditions from a non-Talmudic source, but ancient and trustworthy.
Per that tradition, Tekoa, from the above mishna, was in the Upper Galilee, and it supplied oil to the Temple already in the time before the Chashmonaim. The oil for the menorah was made with purity, therefore there were Jews there that kept mitzvot and knew halacha.
This Tekoa is mentioned in another mishna, albeit a later one, but still from the time of the Temple, bearing witness of Nitai, man of Tekoa, who brought challah from Beitur and they didn't accept from him. The man dwelled in Bei-Yetur, meaning, one of the areas within the land of the Itureans in Lebanon...we should think that this man settled in Bei-Yetur after the conquests of Aristobulus and that he wasn't from Tekoa in Judea, but from Tekoa of Asher, near the land of the Itureans.
Another piece of evidence that Tekoa was in the Upper Galilee, is from the Tosefta in Shevi'it:
"One may eat olives until the last one is finished in Tekoa. Rabbi Eliezer ben Yaakov says: Also that of Gush Chalav."
In a parallel baraita it says:
"One may eat olives until they are finished from Meron and Gush Chalav."
The second baraita lists two famous cities in the Upper Galilee and Meron is parallel to Tekoa in the tosefta, therefore, there is no doubt that the halacha is talking about the Galilean Tekoa, as it is mentioned together with Gush Chalav."
To sum up, we see that there was an ancient tradition that the oil for the Menorah was brought from the Galilean Tekoa, a way's length of four days one direction, meaning it took eight days for someone to go all the way there and return with pure oil.