As Avraham recovers from his circumcision, the temperature gets blazingly hot, with the intention that Avraham relax and recover.

. וַיֵּרָא אֵלָיו ה’ בְּאֵלֹנֵי מַמְרֵא וְהוּא יֹשֵׁ בפֶּתַח הָאֹהֶל כְּחֹם הַיּוֹם. וַיִּשָּׂא עֵינָיו וַיַּרְא וְהִנֵּה שְׁלֹשָׁה אֲנָשִׁים נִצָּבִים עָלָיו וַיַּרְא וַיָּרָץ לִקְרָאתָם מִפֶּתַח הָאֹהֶל וַיִּשְׁתַּחוּ אָרְצָה

Hashem appeared to him in the plains of Mamre; and he was sitting at the entrance of the tent when the day was hot. He raised his eyes and noticed three men were approaching him, and he saw them. He ran toward them from the entrance of the tent, and he prostrated himself to the ground.

His location “from the entrance of the tent” is established when the setting is described, yet repeated when he departs. Why?

The Kehilas Yitzchak explains that the Gemara in Brachos teaches that one who  leaves a synagogue should not take large steps while leaving - he shouldn’t appear happy when finishing a mitzvah. There is also a halacha in he Shulchan Aruch that it is a mitzvah to run towards any mitzvah.

If someone is switching from one mitzvah to another, should he run or not? A paradox is presented:  if he runs, it appears to devalue the first mitzvah; if he doesn’t run, then he isn’t doing the mitzvah of running to perform the second mitzvah!

The resolution is that if the first mitzvah is greater than the second, then he shouldn’t run; so as to not devalue the first and greater mitzvah. If the second mitzvah is greater, the he should run in order to fulfill the second greater mitzvah with haste and zeal. What if the two are equal? He should walk the first half of the journey and run the second half, in this way he fulfills both his obligations.

So how did Avraham conduct his behaviour? The Gemara in Shabbos teaches that taking in guests is greater than speaking to Hashem.

If so, when Avraham went to take in guests, although previously speaking to Hashem, the second mitzvah was greater than the first, Avraham had to run the entire journey.

Therefore the Torah writes that he ran towards them to praise his eagerness to run towards the second mitzvah the entire journey; “from the entrance of the tent”.

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In Parshas Chukas, 19:2, it says: זֹאת חֻקַּת הַתּוֹרָה אֲשֶׁר צִוָּה יְ־הֹוָ־ה לֵאמֹר דַּבֵּר אֶל בְּנֵי יִשְׂרָאֵל וְיִקְחוּ אֵלֶיךָ פָרָה אֲדֻמָּה תְּמִימָה אֲשֶׁר אֵין בָּהּ מוּם אֲשֶׁר לֹא עָלָה עָלֶיהָ עֹל - This is the statute of the Torah which the Lord commanded, saying, Speak to the children of Israel and have them take for you a perfectly red unblemished cow, upon which no yoke was laid.

Rashi states, זאת חקת התורה: לפי שהשטן ואומות העולם מונין את ישראל לומר מה המצוה הזאת ומה טעם יש בה, לפיכך כתב בה חקה, גזירה היא מלפני ואין לך רשות להרהר אחריה-  This is the statute of the Torah: Because the Satan and the nations of the world will taunt the Jews and ask the Jews about their commandments and subsequent purposes.  Therefore, the Torah uses the term decree. I have decreed it; you have no right to challenge it.

This answer seems to imply that there is no reason for this commandment of Parah Admuah; we simply keep it out of blind faith. Rashi 19:22 states in the name of Rabbi Moshe HaDarshan that it atones for the sin of eigel (the golden calf). We are left with a question; is it a chok or to atone for eigel?

The Bikurei Avraham and Kehilas Yitzchak answer that all the different explanations for Parah Adumah (the red heifer) conclude that it atones for eigel, precisely because Parah Adumah has no reason. The sin of eigel was that the Jews threw off the yoke of heaven, so the equal and opposite would be to accept the yoke of heaven despite not knowing the reason.  Thus, both answers ring true - we don’t know the reason for Parah Adumah, and that’s why it atones for eigel.

The Panim Yafos says that the Gemara (Brachos 55a) writes that recalling a previous sin reopens the investigation and it comes under scrutiny again to some degree. This is what the nations of the world and the Satan accomplish when they ask whats the Parah Adumah is for. They know its because of the eigel; therefore we say it’s a chok.
R’ Chaim of Alexander writes that the pasuk says “leimor” (saying) twice-  וַיְדַבֵּר הֹ אֶל מֹשֶׁה וְאֶל אַהֲרֹן לֵאמֹר (And Hashem said to Moshe and Ahron saying) and זֹאת חֻקַּת הַתּוֹרָה אֲשֶׁר צִוָּה הֹ לֵאמֹר (These are the decrees of the Torah that Hashem commanded, saying).  He explains that it is so because of the two answers. If the nations of the world and the Satan ask, its a chok. If Rabbi Moshe Hadarshan is asking, then we have a great reason.