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In Parshas Vayeitze, Rashi comments on the words דרך שבעת ימים, quoting a midrash, saying

כל אותן ג' ימים שהלך המגיד להגיד ללבן הלך יעקב לדרכו, נמצא יעקב רחוק מלבן ששה ימים, ובשביעי השיגו לבן. למדנו שכל מה שהלך יעקב בשבעה ימים הלך לבן ביום אחד

He explains that Yaakov started three days away from Lavan and he had a three day head start on him as he was walking away from him, so Yaakov was 6 days ahead. And Lavan caught up to him on the seventh day, implying that Lavan covered in one day what Yaakov covered in 7 days.

This doesn't seem to make sense to me. Lavan left on the fourth day, so it seems to me he was walking not 1, but rather 4 days by the time he caught up to Yaakov. That would mean he was moving roughly twice as fast as Yaakov, which seems completely reasonable since he wasn't laden with children and animals in his pursuit. How does Rashi's statement that Lavan was moving 7 times as fast as Yaakov work?

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    I think בשביעי השיגו is including the 3 days there already was between them. If Yaakov traveled a mile a day, starting at a distance of 3 miles, Lavan caught him 3 days later, in the 7th mile.
    – shmosel
    Commented Nov 24, 2023 at 21:28
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    Also note that the messenger wouldn't have been laden with children and cattle and it still took 3 days.
    – shmosel
    Commented Nov 24, 2023 at 21:32

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דרך שבעת ימים doesn't mean "after Yaakov had fled for 7 days." If it was describing the length of time, it would have said שבעה ימים (or ארבעה ימים, starting from Lavan's departure). דרך שבעת ימים means Lavan traveled "7 days' distance," i.e., the distance normally covered in 7 days. Rashi is saying that if Lavan only had to travel 7 days' distance to reach Yaakov, he must have covered it in a single day, because Yaakov was already 6 days away when Lavan set out.

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If lavan was 3 days to (for example) the north of Yaakov, and Yaakov was traveling to the south, then this would be the timeline:

During the first three days:

Yaakov is traveling south, a messanger goes north to Lavan and tells him that Yaakov left.

During the next three days:

Yaakov is now 6 (slow) days to the south of his original camp, and Lavan reaches Yaakov's camp.

On the seventh day:

Yaakov reaches Har Hagil'ad, and so does Lavan.

Meaning, Lavan traveled from Yaakov's camp to Har Hagil'ad in 1 day, a trip that took Yaakov (+ family, slaves, and cattle) 7 days to make.

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