Q. (On Asarah Beteveth on Friday this year) if someone davens mincha early, can he then make an early Shabbat and eat before nightfall?
A. Shulchan Aruch (O.H. 249:) quotes an opinion that even on a taanis tzibur (communal fast) you only have to fast on erev Shabbos until you exit the shul after kabbolas Shabbos, past plag hamincha (one and one quarter hour before nightfall). However the Remoh rules that on a communal fast day such as the Tenth of Teves, you should complete the fast until nightfall.
Nitey Gavriel (Chanukah 63: 7) maintains that in the U.S.A. when needed, you can end this fast about a half an hour after the shkiah (ten minutes suffice in Israel). Some Poiskim (Yitzchak Yranen 41) are more lenient and follow the first opinion of the Remoh (above) and permit ending the fast at the shkiah.
Horav Shlomo Miller's Shlit"a opinion is that Ashkenazim should follow the opinion of the Remoh and fast until nightfall, however, if someone usually keeps Rabeinu Tam's timetable, in this case he does not have to wait the full seventy-two minutes.
Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit"a