In Judaism, there are three main fixed prayers per day: the evening prayer after sunset, when the new day begins (“aravit”), the morning prayer (“shah’arit”) and the end-of-day prayer (“minh’ah”).
The Berakhot treatise (“Blessings”) of the Babylonian Talmud, which speaks very abundantly of the hours and forms of fixed prayer, is also interested in its origin: who instituted these three daily prayers?
Then two different opinions appear (which is quite normal in the Talmud!):
Rabbi Yossei, son of rabbi Hanina, said: The practice of praying three time a day is ancient […] they were instituted by the Patriarchs. R. Yehoshua ben Levi said: The prayers were instituted based on the daily offerings sacrificed in the Holy Temple. (Babylonian Talmud, Berakhot 26a)
Rabbi Yossei, quoting some biblical verses, explains that Abraham instituted the morning prayer, Isaac the one at the end of the day and Jacob the evening prayer. Rabbi Joshua explains that the prayers were instituted in parallel with the sacrifices that took place at the Temple in Jerusalem. There were indeed, in the Temple of Jerusalem, two great sacrifices (“tamid”): that of the morning and that of the evening. After some discussion, the Talmud concludes that the Patriarchs instituted the prayers and the rabbis associated these prayers with the sacrifices of the Temple: the emphasis is mainly on the morning prayer and the prayer at the end of the day, which correspond to the two great sacrifices.
The New Testament, the Acts of the Apostles in particular, shows this traditional Jewish life. Jesus’ first disciples, all Jews, continued their Jewish practice while introducing the breaking of the bread, the Eucharist: “They devoted themselves to the apostles’ teaching and to fellowship, to the breaking of bread and to prayer.” (Acts 2:42) The prayers mentioned here are Jewish prayers, so the disciples went up to the Temple (Acts 3).
At the very moment (probably after the destruction of the Temple) when the rabbis matched the fixed prayers with the two great sacrifices of the morning and the end of the day (cf. Talmud above), the Fathers of the Church, inheriting this Jewish tradition, gradually set up their cycle of fixed prayers, what is called the Liturgy of the Hours:
Since the apostolic age the Church has developed her own daily prayer according to an ordered rhythm which covers the entire day, assuming in a new way the liturgical practices of the Temple of Jerusalem. It is certain that the two main canonical hours (Morning Prayer and Evening Prayer) have been drawn also in relation to the two daily sacrifices of the Temple: the morning one and the evening one.
The liturgy of the Christian hours but also the Jewish liturgy are thus both continuations of the Temple liturgy and mainly of the two great sacrifices of the morning and the end of the day.
Over the centuries, the Church has then enriched its liturgy of the hours, while remaining within the framework of Jewish prayer that existed in apostolic times:
Also the prayers of Tierce [mid-morning], Sext [midday] and None [mid-afternoon] correspond to as many moments of prayer of the Judaic practice. On the day of Pentecost, the Apostles were gathered in prayer at the Third Hour (cf. Acts 2:15). Saint Peter had the vision of the sheet descending from heaven, while he was at prayer on a terrace towards the Sixth Hour. On another occasion, Peter and John were going up to the Temple to pray at the Ninth Hour (cf. Acts 3:1).
The prayer of the Christian liturgy of the hours as it has existed for centuries in the universal Church, as sung daily by priests, monks and religious, therefore has its origin in Jewish prayer. A Christian may then discover that he continues, through the sacrifice of his lips, the sacrifices of the Temple of Jerusalem next to his Jewish brothers. A Jew may discover that Christians still live today by a living Jewish tradition. Praying side by side at the same time already means a mysterious orientation towards the same hope.
 In the biblical—and Jewish—conception of time, the new day begins and ends at sunset.