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The travel pace description and table on page 181-182 of the Player's Handbook states that a normal travel day may contain 8 hours, and gives the following table:

 Pace:   /Hour    /Day         Miles in an 8-hour walking day:
  Fast   4 miles  30 miles --> 4x8 = 32 miles (-2 miles a day)
Normal   3 miles  24 miles --> 3x8 = 24 miles (OK)
  Slow   2 miles  18 miles --> 2x8 = 16 miles (+2 miles a day)

Why is there an difference of 2 miles for fast and slow pace?

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So that miles/day can be multiples of 6, to translate into integer values for hexes/day on kingdom and continent scales.

For kingdom maps, 1 hex = 6 miles so:

  • Fast = 5 hex/day
  • Normal = 4 hex/day
  • Slow = 3 hex/day

For continent maps, 1 hex = 60 miles so:

  • Fast = 2 days / 1 hex
  • Normal = 5 days / 2 hexes
  • Slow = 10 days / 3 hexes

If you're not a multiple of 6, then it can get more complicated with the math. And while I'd love to do the math, some people think it's not as fun as I do.

This answer " Do the map scales suggested in the DMG tie into any rules? " gives some insight to this. It seems to just be a matter of convenience when traveling across maps that follow the scales recommended in the Dungeon Master's Guide (as well as, I assume, some pre-made campaigns which follow the DMG guidelines).

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The book does not say, and I found no develop commentary; speculation follows:

It does make some sense that the faster pace would result in less than the expected number of miles and the slower pace would result in more than the expected number (walking faster is harder, and walking slower is easier). So that's one small potential reason for the difference.

Also, as user Mathaddict pointed out in their answer, it is likely so that all the numbers are divisible by 6, making them far more useful for hexagonal grids.

And that's about all I can think of... The only other thing to I would note is that these are all approximations anyway, and not very good ones at that:

Here is the DnD Beyond version of the table: Travel Pace Table

The "Distance per Hour" entries are all rounded down from what we would calculate using the "Distance per Minute" entries (4.54, 3.41, and 2.27 miles).

Furthermore, if we take the 400 foot pace and extend it to 8 hours, we would get 192,000 feet, or 36.363636 miles.
Similarly, with the normal pace of 300 feet, we'd actually get 27.272727 miles.
And with the slow pace of 200 feet, we'd get 18.181818 miles.

This isn't any sort of reason for why the numbers are wrong, I'm just pointing out that even if they were "right" going off the "Distance per Hour" entries, they would still be wrong going off the "Distance per Minute" entries. More accurate Distance per Day entries would likely be 36/27/18

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