Related על ברכות 4:1

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].”

...The evening prayer [of Shmoneh Esreh] does not have a set time. Rebbi Elazar Bar Yossi says, “[A person should pray the evening Shmoneh Esreh] with the closing of the gates [of the Bet Hamikdash (Temple)].” Rebbi Elazar Bar Yossi said, “My father [always] prayed [the evening Shmoneh Esreh] with the closing of the gates [of the Bet Hamikdash].” [A person] who prays the Mussaf prayer [of Shmoneh Esreh] either after the morning Tamid [sacrifice] has been brought or before the morning Tamid [sacrifice] has been brought, has fulfilled his obligation [of praying the morning Shmoneh Esreh on time.]

I would have thought that [a person] should pray [Shmoneh Esreh] in a loud voice. [However] it explains by Chana, “and Chana was talking in her heart…” (I Samuel 1:13) I would have thought [a person] may pray all [three Shmoneh Esreh] in one shot. [However] it explains by David, “Evening, and morning, and afternoon…” (Psalms 55:18) Evening that is the Maariv prayer, morning that is the Shacharit prayer, and afternoon that is the Mincha prayer. I would have thought that [first a person] should ask for his [personal] needs and then he [should] pray [the established text of Shmoneh Esreh] and go away [from standing in front of God]. [However] it explains by Shlomo, “… to hear the song and the prayer …” (I Kings 8:28) Song that is the song,4 prayer that is the request. And so it says, “Sing before Hashem…” (Psalms 33:1)