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This is going to be my version of the diatance between Suna and Konoha.

To start off, there are two part that I have to prove before doing the actual calc.

  • Ability to maintain FTE movement.
  • Amount of Rest

MAINTAINING FTE MOVEMENT
So, recently in the thread discussing this feat , certain users argued that Kakashi, Naruto, Sakura and Temari, despite being shown leaving Konoha at FTE speeds in a rush to make it to Suna, didn't maintain their FTE speeds. They claimed that there was no proof that they could and this is just not true. 
Shunshin is the Jutsu by which Naruto Characters achieve these FTE speeds and it states the following:

Shunshin

Body Flicker Technique (Shunshin no Jutsu)
Ninjutsu, D-rank, Supplementary

Users: Gaara, Hatake Kakashi, et al

A movement technique with extreme speed like a gust of wind!!

Appearing along with the wind, disappearing like the wind: the ninja’s instantaneous movement technique. This super fast movement is almost impossible to grasp with the naked eye. If seen by an ordinary person, it would seem as if the user has teleported… In reality, the user has vitalized his body with chakra and moved at super speeds. The amount of chakra used up differs depending on the distance and elevation of their stopping point in comparison to the starting point.

The cloud of sand dances in the wind…

Haku’s and Kakashi’s Body Flicker. Dancing leaves and disappearing in an instant like mist.

There are many variations of the Body Flicker for the various villages and user. Gaara’s use includes the Sand Body Flicker. There are also the Mist Body Flicker, Water Body Flicker, and Leaf Body Flicker, among many others.

As we can see, Shunshin itself poses no limitation other than Chakra and this is a D-Rank Jutsu which is low impact on them. In the Manga on multiple occasions we see ninja maintaining Jutsu of the same rank and higher for hours up to several days:

  • Oboro: Could maintain his Haze Clone Technique which, like Shunshin, is a D-Rank Jutsu for an entire night without any trouble or adverse affects (Scan 1 | Scan 2 | Scan 3 ) And Naruto himself maintained Shadow clones in addition to transformation jutsu all the while (A B- Rank and C-Rank Jutsu respectively).
  • SA HQ with Ao, Inoichi and others maintaining the Sensing Sphere 

These are just 3 examples of many throughout Naruto. With what's established in verse, this is proof enough that Shunshin can be maintained. But in addition to this, Kishi himself supports this notion via his own statements:

Kishimoto: It would actually take too long to really go nitty-gritty into details, but for example: one of the things I focused on was that anything that's NOT possible to recreate, or to do, using ninjustu, ninja skills, I would not develop for Naruto's world. So no cars. Because they have shuriken, the throwing stars, there's no guns either. So there were certain things I had clearly in my head that I didn't want to have available in their worldview.

Taken from here

For reference, the High-Way Speed Limit  in Japan is 62 mph (27.7 m/s). 

NOTE: For Reference, Keep in Mind that Every Naruto Speed Feat with Shunshin calced is Casually Above Supersonic.

AMOUNT OF REST

Just like in the thread, the amount of rest is important also to the feat, but "How huch of it?" is the point of contention here. 8 hours of sleep is being tossed around as an arbitrary assumption here, but this assumption is not correct. Ninja in Naruto are a military force and military trained. They're not normal people and IRL, soldiers at home or deployed abroad rarely get 8 hours of rest a day. So holding Ninja to a standard for ordinary people when irl we don't even do so with our own Military Forces is blatantly fallacious and shouldn't be done. 

Instead of assuming values I actually did some research and found that (1) 4 hours of sleep per 24hr cycle is the least amount of sleep needed to survive and (2) studies and articles have shown and stated Military Forces get less than 5 hours of sleep per day with lots of soldiers citing  around 4 hours of sleep, which lines up with the Military belief in the "4 Hour Rule", which i'm sure some of you have heard of before. 

Sources:

https://www.ncjrs.gov/App/Publications/abstract.aspx?ID=244885&fbclid=IwAR1y0vlsAwh6UbUmL8xyUPhCfKoK8sBLtC9TL6LCL7v-t0g8DGrfNIJJgow

https://www.sleepfoundation.org/articles/do-soldiers-get-enough-sleep?fbclid=IwAR0QpkFNMycG4ogCGjJC6Gg-qZEnfNz2FD-iCMfcCNGWvoDoi6sacjef6Y0

https://www.sleep.org/articles/military-sleep-issues/?fbclid=IwAR0jNj6SzCyE-_x8qLE_O-HjjZrI86GSjxD7WfpLG-SsneVcElo_MaK8yCM

https://www.quora.com/When-on-the-front-line-how-many-hours-do-soldiers-sleep-a-night-Can-they-fall-asleep-even-in-fear?fbclid=IwAR0nngHa2tkXEK5VD8Pb6xxp99CsYO0bpjYznR9lVRVr2nF8KWzMlvb_pUc

Ontop of this, in Verse, Naruto characters (Genin) way back since part 1 have been shown going 24+ to over 26+ hours without sleep or much rest, food or water and were just fine and in their cases they were travelling or fighting battles. Naruto himself went from Traveling all day nonstop on the 4th day of CE to fighting team Oboro all night to Continuing travelling to the Building to going straight into preliminary battles to going across the village to find kakashi to going with Ebisu to a training location to continuing training with Jiraiya, all before being shown to have had rested (Note, the Bolded was a 26 hr timeframe by itself). And it wasn't just Naruto who demonstrated going this length of time himself, but all Genin. 

So, taking all of this into consideration, 8 hours of sleep per 24hr cycle when they were in an Urgent Mission is too much and nonsensical in the context of the story and IRL if you think about it if the situation were the same. 

Based on all of this, 4 hours of sleep per 24hr cycle is most accurate and 2 hours for resting and eating per 24hr cycle is more than generous considering:

  • Catching Your Breathe
  • Restroom Breaks
  • Eating/Drinking

Doesn't take 2 hours (Even in sports training, this is not a thing). And I'm not even assuming Naruto and Co took Military Ration Pills which logically they would've given the Urgency of the Mission. 

So on to the calc....

THE CALC

I want to preface by saying both of these are technically "Low-Balling" since the Verse is proven and portrayed much faster. 

Things to Note

  • The only real assumption being made in this calc is the length of "Rest Time", which is High-Balled to 2 hours.
  • Naruto and Co made it to Suna in 60 hours (They left the village the same day Kankuro was defeated and given a 2-3 day timeframe to live and made it when he had 12 hrs left. 
  • This is going to use FTE Speed as the High-End (Due to Naruto and Co being shown Leaving the Village at FTE Speeds) and 27.7 m/s as the Low-End (And note, Unlike other verses with similar showings, notably Bleach with Seireitei and Hueco Mundo, Naruto characters are actually Shown doing so at FTE speeds which makes the High-End more accurate according to the showings).
  • 12 hrs instead of 16 hrs will be subtracted from the Time to factor in Sleeping, Eating/Dringing, Restroom Breaks and Catching breathe. 

Calc 1: FTE Method:

  • Distance = Speed * Time
  • Speed = 34.3 m/s
  • Time = 48 hours
  • 34.3 m/s * 48 hrs = 5927.04 km

Calc 2: Kishi's Statement Method:

  • Disntance = Speed * Time
  • Speed = 27.7 m/s
  • Time = 48 hours
  • 27.7 m/s * 48 Hrs = 4786.56 km

_________________________________

RECAP:

Distance from Konoha to Suna is...

  • High-End: 5927.04 km
  • Low-End: 4786.56 km

NOTE: I edited the high-end to reflect @Damage's response as well as after discussing with Alex.

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