Prayer Of Distress Prayer Of Mincha

וְיִצְחָק֙ בָּ֣א מִבּ֔וֹא בְּאֵ֥ר לַחַ֖י רֹאִ֑י וְה֥וּא יוֹשֵׁ֖ב בְּאֶ֥רֶץ הַנֶּֽגֶב וַיֵּצֵ֥א יִצְחָ֛ק לָשׂ֥וּחַ בַּשָּׂדֶ֖ה לִפְנ֣וֹת עָ֑רֶב וַיִּשָּׂ֤א עֵינָיו֙ וַיַּ֔רְא וְהִנֵּ֥ה גְמַלִּ֖ים בָּאִֽים

וַיְהִ֗י אַֽחֲרֵי֙ מ֣וֹת אַבְרָהָ֔ם וַיְבָ֥רֶךְ אֱלֹהִ֖ים אֶת־יִצְחָ֣ק בְּנ֑וֹ וַיֵּ֣שֶׁב יִצְחָ֔ק עִם־בְּאֵ֥ר לַחַ֖י רֹאִֽי

Why do we need to be informed of Yitzchak's presence in באר לחי ראי?  

The name באר לחי ראי originates from when Hagar is sent away by Sarah and the malach appears to her and says she will have Yishmael.  The possuk says וַתִּקְרָ֤א שֵׁם⁠־י״י֙ הַדֹּבֵ֣ר אֵלֶ֔יהָ אַתָּ֖ה קל ראי.  Onkelus says she was praying to Hashem and refering to Him as the one who sees all.  The Targum Yonasan adds דחמי ולא מתחמי, the One who sees but is not seen.  The next possuk says  עַל⁠־כֵּן֙ קָרָ֣א לַבְּאֵ֔ר בְּאֵ֥ר לַחַ֖י רֹאִ֑י.  Rav Hirsch notes the addition of the word לחי to include all of time and the change in vowel from Hagar saying רֳאִ֑י to רֹאִ֑י to indicate Hashem sees every person, He sees me at all times.  The spot of באר לחי ראי is the place where Hagar prays to Hashem.  It is a place she designated for prayer.  The Seforno says that is why Yitzchak chose that as his place to pray for it was already designated as a place of prayer. Rav Hirsch notes the strange phrase בָּ֣א מִבּ֔וֹא, "he came from coming," indicates that he felt the need, he was drawn to באר לחי ראי to pray for his own match as this was the place that the family has heard am message from Hashem beforehand in the case of Yishmael, and now he was coming home from being drawn to באר לחי ראי.  The next possuk, וַיֵּצֵ֥א יִצְחָ֛ק לָשׂ֥וּחַ בַּשָּׂדֶ֖ה, Chazal identify as Yitzchak praying.  However, the line also demonstrates the difference between the prayer of Hagar and that of Yizchak.  

Hagar prays to Hashem in times of great distress.  However, as the Targum Yonasan says, she doesn't see Hashem in other words, she is not always cognizant of His presence in her life.  In times of upheaval she calls out to Hashem.  Rashi says Yitzchak went to באר לחי ראי in order to bring Hagar so that Avraham could marry her again.  Hagar still lives in באר לחי ראי, that is her world view.  

At the Akedah it says וַיִּקְרָ֧א אַבְרָהָ֛ם שֵֽׁם⁠־הַמָּק֥וֹם הַה֖וּא י״י֣ ׀ יִרְאֶ֑ה אֲשֶׁר֙ יֵאָמֵ֣ר הַיּ֔וֹם בְּהַ֥ר י״י֖ יֵרָאֶֽה.  Avraham didn't merely acknowledge that Hashem sees us but ה יראה, will be seen.  We see Hashem.  As the Gemarah Chagigah (2a) says יראה יראה כדרך שבא לראות כך בא ליראות מה לראות.  Avraham and his descendants don't just know of Hashem's presence but they see Hashem as part of their life.  This is what is represented by the mincha prayer of Yitzchak.  It is not the beginning or end of the day where it is more understandable to start out the day with a prayer or bookend with a prayer when one is not tarried, it is the prayer in the middle of the day.  In the midst of one's activities, one recognizes the Hand of Hashem in one's activities.  וַיֵּצֵ֥א יִצְחָ֛ק לָשׂ֥וּחַ בַּשָּׂדֶ֖ה.  This is a mere שיחה not in the context of a more formal prayer yet even in such a situation Yitzchak prays to Hashem.  Yitzchak transforms prayer into an integral part of one's activities (based upon Mimamakim by Rabbi Mandelbaum, post of Rabbi Rudman.) 

(The Kli Yakar says that the prayer of mincha is readily accepted because it is in the middle of the day removed from the time of night which is strive judgement.  Rav Shmuel Eliyahu takes the opposite approach.  He explains that mincha is compared to ketores, תִּכּוֹן תְּפִלָּתִי קְטֹרֶת לְפָנֶיךָ מַשְׂאַת כַּפַּי מִנְחַת עָרֶב (Tehillim 141:2)  because just as ketores has the ability to nullify strict judgement as seen when Aharon was told to use ketores to heal the nation, so too the prayer of mincha has the ability to nullify the time of strict judgement which is present in the afternoon.)