Why did Eliezer run after Rivkah?

Two different approaches, which may demonstrate different approaches to peshat. In Chayei Sarah:

יז וַיָּרָץ הָעֶבֶד, לִקְרָאתָהּ; וַיֹּאמֶר, הַגְמִיאִינִי נָא מְעַט-מַיִם מִכַּדֵּךְ.

17 And the servant ran to meet her, and said: 'Give me to drink, I pray thee, a little water of thy pitcher.'

But why bother to run, and why does the pasuk bother informing us that he did it, if he did? One approach is that of Rashi, who relies on Midrash Rabba. Rashi writes that he did it because of a miracle that he saw:

And the servant ran toward her: Because he saw that the water had risen toward her. — [Gen. Rabbah ad loc.]

וירץ העבד לקראתה: לפי שראה שעלו המים לקראתה:

This is based on Bereishit Rabba:

ותרד העינה ותמלא כדה ותעל
כל הנשים יורדות וממלאות מן העין, וזו כיון שראו אותה המים, מיד עלו.
אמר לה הקב"ה: את סימן לבניך, מה את, כיון שראו אותך המים מיד עלו, אף בניך כיון שהבאר רואה אותן, מיד תהיה עולה.
הה"ד: (במדבר כא) אז ישיר ישראל את השירה הזאת עלי באר.
___________________________

וירץ העבד לקראתה

לקראת מעשיה הטובים.

Thus, based on a derasha on the previous pasuk about the miraculous rising of the water (vataal), the servant ran towards her good deeds, which she must have to merit this miracle over all other women. There is also the rereading of likrata as likrat her good deeds. This is somewhat midrashic, but if the events indeed happened, then it can make for a good close reading and midrashic peshat. (And given that the rest of the pasuk is essentially praise of Rivkah's various maalot, interpreting the end of it in this way is simply following the set precedent.)

Ibn Caspi writes that he ran towards her because she was so beautiful.

וירץ העבד לקראתה. בעבור שראה אותה טובת מראה מאד:

Thus, if all sorts of girls might pass his test, he should approach a pretty girl first. Or else, since he saw she was so pretty, he hoped that she was the one for Yitzchak, and so he ran up to her.

What motivates Ibn Kaspi here? I would guess that once Rashi explained vayaratz in this midrashic manner, but labelled as peshat, he felt compelled to address the same textual feature from a more peshat-oriented perspective. Now, the previous pasuk was:

טז וְהַנַּעֲרָ, טֹבַת מַרְאֶה מְאֹד--בְּתוּלָה, וְאִישׁ לֹא יְדָעָהּ; וַתֵּרֶד הָעַיְנָה, וַתְּמַלֵּא כַדָּהּ וַתָּעַל.

16 And the damsel was very fair to look upon, a virgin, neither had any man known her; and she went down to the fountain, and filled her pitcher, and came up.

and context should play a role in explaining the vayaratz which begins the pasuk. For Rashi and the Midrash Rabba, it was the end of the pasuk, vataal. Ibn Caspi needs something from that pasuk, and so he goes to the beginning of the pasuk, and sees how she is described as exceptionally pretty.

From my perspective, Rashi is closer to peshat here than Ibn Caspi. It seems farfetched that her prettiness was the cause of his running. Rather, it was some sort of miracle. Ibn Caspi's problem was that he didn't look back far enough. The preceding pasuk was:

טו וַיְהִי-הוּא, טֶרֶם כִּלָּה לְדַבֵּר, וְהִנֵּה רִבְקָה יֹצֵאת אֲשֶׁר יֻלְּדָה לִבְתוּאֵל בֶּן-מִלְכָּה, אֵשֶׁת נָחוֹר אֲחִי אַבְרָהָם; וְכַדָּהּ, עַל-שִׁכְמָהּ.

15 And it came to pass, before he had done speaking, that, behold, Rebekah came out, who was born to Bethuel the son of Milcah, the wife of Nahor, Abraham's brother, with her pitcher upon her shoulder.

Thus, he had just set the test, and all of a sudden, this beautiful young girl appeared with a pitcher on her shoulder, with ala mayles, seemingly ready to pass his declared test. This was surely the hand of God and so, excited, he ran to her. This is not precisely Rashi, but it is along those lines.

What follows was originally going to be a separate post, but it is related enough, and so I will put it here. Perhaps we can get to the bottom of the question of just why Eliezer ran after Rivkah. What was his hurry? After all, he surely made good time before this! Didn't he have kefitzas haderech? Couldn't he have calmly walked up to Rivkah?

I think the answer might be that this is just the reason for the hurry. As we see a bit later:

נו וַיֹּאמֶר אֲלֵהֶם אַל-תְּאַחֲרוּ אֹתִי, וַה' הִצְלִיחַ דַּרְכִּי; שַׁלְּחוּנִי, וְאֵלְכָה לַאדֹנִי.

56 And he said unto them: 'Delay me not, seeing the LORD hath prospered my way; send me away that I may go to my master.'

If Hashem is prospering his way, things are on a roll. Why delay? Why even tarry all night, as in the previous pasuk.

Indeed, Eliezer is by no means the only one to hurry. We have the following people, all in a terrible rush. First, Eliezer hurries to her:

יז וַיָּרָץ הָעֶבֶד, לִקְרָאתָהּ; וַיֹּאמֶר, הַגְמִיאִינִי נָא מְעַט-מַיִם מִכַּדֵּךְ.

17 And the servant ran to meet her, and said: 'Give me to drink, I pray thee, a little water of thy pitcher.'

Then, Rivkah hurries to give him a drink:

יח וַתֹּאמֶר, שְׁתֵה אֲדֹנִי; וַתְּמַהֵר, וַתֹּרֶד כַּדָּהּ עַל-יָדָהּ--וַתַּשְׁקֵהוּ.

18 And she said: 'Drink, my lord'; and she hastened, and let down her pitcher upon her hand, and gave him drink.

and then she hurries to fill the trough, and runs to the well to draw water again:

כ וַתְּמַהֵר, וַתְּעַר כַּדָּהּ אֶל-הַשֹּׁקֶת, וַתָּרָץ עוֹד אֶל-הַבְּאֵר, לִשְׁאֹב; וַתִּשְׁאַב, לְכָל-גְּמַלָּיו.

20 And she hastened, and emptied her pitcher into the trough, and ran again unto the well to draw, and drew for all his camels.

Then, Rivkah runs to her mother's house:

כח וַתָּרָץ, הַנַּעֲרָ, וַתַּגֵּד, לְבֵית אִמָּהּ--כַּדְּבָרִים, הָאֵלֶּה.

28 And the damsel ran, and told her mother's house according to these words.

and then, when Lavan hears, he runs to Eliezer by the fountain:

כט וּלְרִבְקָה אָח, וּשְׁמוֹ לָבָן; וַיָּרָץ לָבָן אֶל-הָאִישׁ הַחוּצָה, אֶל-הָעָיִן.

29 And Rebekah had a brother, and his name was Laban; and Laban ran out unto the man, unto the fountain.

So everyone is in a big rush. I believe that the intent is to heighten the emotion and intensify the pace of the narrative. She runs to her mother's house because she is excited at the news and the gifts. And Lavan is also excited and runs to Eliezer. And furthermore, to show how all this is clockwork in the Divine plan. No one should delay, since Hashem has prospered Eliezer's way. (A metaphorical kefitzas haderech.)

And so Rivkah's coming out with the pitcher just after he set the test is an example of this prospering of the way, and so his excitement and his hurry to play his part fits in with all of this. But that the running was a much broader phenomenon should certainly factor into our analysis of why Eliezer is running.