Related for Beitzah 33:2

If the holiday of the beginning of the year falls on a Sabbath, the school of Shammais says: One prays ten [Benedictions]; but Hillei's school says: One prays nine. If a holiday falls on a Sabbath, the school of Shammais says: One prays eight. One says that of the Sabbath by itself and that of the holiday by itself and begins with [the] Sabbath [formula]. But Hillel's school says: One prays seven; one begins with [the] Sabbath [formula] and closes with [the] Sabbath [formula] and says the sanctification of the day in the middle. The school of Hillels says to the school of Shammais: In the presence of all of you, the elders of the school of Shammais, Honi the little one did not appear and said only seven [and] all the people said unto him, Well being unto thee? Da said to him- NEN the school Schammais: Because the time was suitable for shortening.' ״ Then Hillei's school said to them: If the time is suitable for shortening the net, then he should have abbreviated all of them

Just like the Torah established a set time to read the Shema, so too the Sages established a set time for [the] prayer [of Shemoneh Esreh]. Why did they say [that] the morning prayer [of Shmoneh Esreh can be prayed only] until noon? Because the morning Tamid (daily offering) [sacrifice] could be brought [only] until noon. Rebbi Yehudah says, “[The morning prayer of Shmoneh Esreh can be prayed only] until [the end of the first] four hours [of the day].” And why did they say that the Mincha (afternoon) prayer [of Shemoneh Esreh can only be prayed] until the evening? Because the afternoon Tamid [sacrifice] could be brought [only] until the evening. Rebbi Yehudah says, “[The Mincha prayer of Shmoneh Esreh can be prayed only] until Plag Hamincha.” And when is Plag Hamincha? Eleven minus one quarter hours [of the day] (i.e. 10 ¾ hours). And why did they say that the evening prayer [of Shmoneh Esreh] does not have a set time? Because the limbs and fats [of the sacrifices] could be brought the whole night. And why did they say that the Mussaf prayer [of Shmoneh Esreh can be prayed] the whole day? Because the Mussaf (additional offering) sacrifice could be brought the whole day. Rebbi Yehudah says, “[The Mussaf prayer can be prayed] until [the end of the first] seven hours [of the day].”