For reasons that are not entirely clear to me, there is some confusion about scales, distance measures and time in fantasy adventure games. Especially in relation to discretized (squares and/or hexes) movement, a wide variety of solutions are discussed. Oftentimes with results that are more complicated than just using a non-discretized map and a ruler, defeating the purpose of discretization. In the following I will  purposefully write out all units, for absolute clarity. 

Instead of looking at the roots of these discussions & misconceptions, I will try to make a case for the simplicity of the so-called „imperial units“ used in AD&D 1e. 

As I have talked about earlier, in a gaming environment, we usually want movement rates given in small integer numbers, with common values falling somewhere between 2-12 movement points per game round. Pseudo-medieval units allow this nicely. 

What is an inch? 

Conceptually, an inch is the width of a thumb pressed down upon a surface. As such, it is a distance measure both practical, easily imaginable and a de-facto standard for miniature bases. Also, it is the de-facto standard of miniature wargaming measurment. 
The concrete values of movement rates come from the interaction with the inch and the standard size of miniature wargaming terrain: a ping-pong table, which is 5ft x 9ft, or (at 12 inch to a foot) 60 inch x 108 inch. As we talk about distances, only linear units, not areas, are of interest. To present ample room for maneuvre, movement rates for miniatures have traditionally been in the range between 6-12 inch per game round for infantry and 12-24 inches per game round for faster units such as cavalry. A slow unit needs 10 rounds to cross the short side of the terrain. Assuming a medieval battle with lines facing each other and some setup space (6 inch from the edge, so a 48 inch gap exists between armies at game start), two opposing forces’ main battle lines will clash with each other after 2-4 (~3) rounds if both march directly at each other (covering 12-24 inch per game round). This is obviously benefial to gameplay and still allows for maneuvre and jockeying for position before shields smash!. 
In wargaming, the time, figure and spatial scales are then adjusted such that the small integer movement rates lines up with what is being modelled. 
From all that, many games, but especially D&D derive their basic infantry movement rates of 6/9/12 inches per game round. Also it is clear, that inch is a „modelling measurement“ in that sense, equivalent to a square or a hex in a boardgame, not to be confused with any potential inches existing in the modelled game world. 

Quasi-medieval movement rates and distance measures 

The ancients and forebears had little use for precise (millimeter) or geodetically defined (1 meter = 1/10 000 000 of the distance from pole to equator) distance measurements. Distance itself was either defined by parts of the body, readily available at the marketplace (thumb [inch], two outstretched arms [fathom], foot [foot] and so on) or by the distance covered during s specified time-frame. A Day’s journey is a unit of distance intuitively understandable since biblical times (1 Kings 19:4 ), for example. 
Naturally those ancients which were inclined to measure more objectively, the Romans, linked travel-distances to body part in a nice and easy way: the mille passum or mile. 

To this very day, militaries teach their soldiers to count double-paces as a tool to measure distances. This is especially useful if no Bematist (sage-like specialistsin AD&D) with bespoke measurment wheels was around. 

The romans thus definded: 
 
1 mile = 1000 double paces. 
1 double pace = 5 feet. 

From that follows: 

1 mile = 5000 feet. 

A very easy concept indeed, linking body parts to activity of marching with a unified distance measure. Now the romans could measure what a peculiar Day’s journey was objectively, and soldiers who were accustomed to counting double paces had a direct, corporeal memory of what a mile was, in turn making guessing distances easy and easy to communicate. For the surveyors, the decimal system behind the mile was also beneficial. Half a mile is 500 double paces and 2500 feet and so on. 

The story does not end here, as there is a natural tendency to consider subdivisions of a marching day. Maybe important stops were each a Day’s journey apart, but many things, maybe even the enemy was mere hours away. As such, many traditions have the concept of the „Hour’s walk“. 

In english parlance the unit used for that is the league. A league is defined as 3 miles. 

1 Hour’s walk =
1 league = 3 miles = 3000 double paces = 15 000 feet= 5000 yards

It is easy to see, how apart from military logistics or surveying, the league was a very useful unit for travellers such as traders or adventurers. Note that the romans used the gallic league at half-an-hour’s walk, directly competing with the roman mile. Medieval leagues are all much closer to the 3 miles/ full hour’s walk. 

It is easy to postulate then, assuming 10 hours of marching time, an average Day’s journey would then be just ten leagues: 
 
Day’s journey (10 hours of travel) = 10 leagues = 30 miles = 30 000 double paces = 150 000 feet. 

If one looks at historical definitions of a Day’s journey we sometimes find values closer to 20-24 miles, assuming 8h of feet travel: 
 
Day’s journey (8 hours of travel) = 8 leagues = 24 miles = 24 000 double paces = 120 000 feet. 

Middle European medieval Day’s journeys differentiated between feet travel and mounted Day’s journeys with a maximum about 38 miles. 

Gary Gygax and the world of Greyhawk 

As I have noted elsewhere, Gary Gygax has a very good handle on spatial situations. He breezes through scale issues, has a very good sense of geography and architecture in both spatial as well as temporal dimensions. He also is a bona-fide wargame designer, to whom it is clear that map-scale, time scale and figure scale have to be adjusted to the available playing space and situation at hand. A further point can be made when looking at the map scales he chose for the world of greyhawk: 

WoG-hex (Darlene Map): Specifically defined as 10 leagues = 30 miles 

Most wilderness distances in Temple of Elemental Evil and the battle descriptions in the Folio are in fact presented in leagues. We can clearly see, that a Darlene-Hex is supposed to be a Day’s journey and that within a subdivision onto leagues aka Hour’s walks is mentally made. So, whatever the actual precise measurements one chooses, the conceptual scales are obviously: 
 
1 hex : hour’s walk 
1 hex : day’s journey 

If we look at other scales chosen, it becomes clear Gygax always thought from the time-scale first, e. g.: 
 
10-foot dungeon squares for game rounds 

240 yard hexes for game turns (Vault of the Drow) 

Suggested time-space scaling for game purposes 

It must be clear, that it would be folly to play individual days on the Greyhawk map, where we could at most move one hex. And it would be inane to play individual hours on a map scaled in leagues. We must always use a larger time scale than our discretized travel time is, so we get ample movement rates. 

If we do want to leverage the advantages of Gary’s foresight and understanding, the human nature of quasi-medieval measurments and the convenience of game rounds, we can use these standard game round length-distance pairings (emphasis added for scales used by EGG in AD&D 1e): 
 
10 foot hexes (squares) for a round (minute) of combat indoors 
10 foot hexes (squares) for a turn (10 minutes) of careful exploration indoors 
10 yard hexes (squares) for a round (minute) of combat outdoors  (Chainmail scale)
100 yard hexes for a turn (10 minutes) of movement outdoors
1000 foot (330 yard) hexes per hour round of movement outdoors 

1 mile hexes for a watch (4 hours) of movement on detailed hex map (this is the half-day’s travel mentioned in the PHB and the 1 mile hexes mentioned in the DMG Wilderness generation sub-system)

1 league hexes for a day of movement on a hex map 

2 league hexes for 2 days of movment on a hex map

5 league hexes for a week of movment on a hex map 

10 league hexes for a fortnight of movement on the Darlene map 

If you use these time-space pairings you can keep the movement allowance of each unit/figure at 

6 inch / 9 inch / 12 inch 
aka 
6 hexes of clear terrain to 12 hexes of clear terrain per game round, i.e. Movement Points. 

Using that scheme, monster speeds can be kept as printed, too. Note how severeley detrimental the tradition of Basic D&D (starting with Holmes) and it’s epigones was stop providing the inch-based movement rates. 

Obeservant readers will note that as we go up that scale-ladder, the average speed decreases. That is intended and realistic, both conceptually as well as empirically. Moving though a hex does not happen in a straight line, so lower scale speeds cannot directly be extrapolated to higher scale speeds. It would be akin to driving at 120 miles per hour on the Autobahn for ten minutes and then extrapolating that average speed to a week-long road trip. Sparing you a long essay on that subject, further excluding explanation why at least a full day of rest per five days of travel are absolutely neccessary if animals are involved and so on, be assured that actual walking or riding speeds are immaterial to overland travel and only (ever downward going) average speeds matter. These are well served with the more abstract &  relative movement rates in inches. 

Terrain 

As I have explained elsewhere, the way to go regarding movement speeds in different terrain is to assign small integer movement point cost for terrain. 

Traditional values are: 

1 Open Ground 

2 Forest, Hills 

3 Swamp, Mountains 

and a bonus for roads that an go from +1 Movement Point for staying on the road the whole game round, or making the terrain effectively open ground while moving along the road, up to just 0.5 movement points per road hex. The latter is effective in modelling things such couriers or a handful of characters on horseback without entourage and magical rest methods. 

Conversely, river crossings beyond bridges should incur a penalty, depending on size of the waterway, ranging from a mere +1 movement cost, to only allowing a river crossing if it takes the full game round.

Note that the ratios implicit in such movement cost is in full agreement of the „time-distance construction kit“ given in the DMG as well as concrete rates of the OD&D LBBs.

Closing remarks 

Once you master the simple pre-configured time-space scales above and in extant products, you can easily start to mess with one of the variables: if you do not mind changing the integer values of movement rates, many bespoke hex-sizes can be used. An example would be halved movment rates in order to use 2 league hexes for situations when you play out just one day per modelled round. Which is what I do to not have to have a jump in hexmap scales. Also, a properly modelled metricized scaling scheme does some rounding: 10 leagues or 30 miles become 50km hexes, which are subdivided by 5 into 10km (2 leagues), which are then subdivided by 5 again into 2km hexes and so on. What we have here are numbers that are not scaled for surveying but conceptual scales, providing easily usable numbers to facilitate actual play.
Furthermore note how the double pace from roman times is exactly 5 feet long, which in turn allows easy acces to what a mile is in the game: 1000 5-foot squares or 500 10-foot squares, with league being three times that. Also not the 1:3 relation among yards and feet, which makes a league exactly 500 outdoor-scale-hexes long. Or in short:

1 mile = 5000 feet [= 500 indoor squares/hexes]
1 league = 5000 yard = 15 000 feet= 3 miles [= 500 outdoor hexes]

Definitions for current miles (= 5280 feet) or double paces (4 feet 10 inches) defeat their ancient & human-scaled purpose and thusly have to be rejected as ungameable. You’d be better off going metric than going current statute mile for your fantasy adventure gaming.