This is crossposted from my answer on a related question over on SFF. I've modified it a little based on discussion in this site and this specific question.
A user on reddit did some calculations to find how long it took for the message to get from the 7 companions to Dany and for Dany to come rescue them. The user estimated it to be around 5 days based on growth rate of ice, the air speed of an
unladen swallow raven, and approximate airspeeds for a Dragon and approximate distances. This answer however has been modified for how long they actually spent on the island. It seems people on this site are more convinced it was shorter and may be more interested in the quick version at the bottom.
Link to the original post
I've broken down their answer but provided a link to the original just above.
- Gendry setting off to them reaching the Island approximately 30 minutes to an hour.
- For there to have been any reason for the wights not to give Gendry chase he must've gotten a significant distance before the wights caught up to the
Fellowship company. They then start running and although IIRC it looks like they run through a canyon, I'd assume they had a bit of a run before they were caught by the wights.
- The Raven likely took around 3 days to get from Eastwatch to Dragonstone.
- A raven flying from Eastwatch to Winterfell would be about a day:
Homing pigeons have been recorded to be able to reach speeds of up to 50mph and although discussions have taken place to the speed of ravens, although no real speed is given, we are led to believe that in-universe ravens are quicker and stronger that in-universe pigeons as stated by Maester Aemon:
Doves and pigeons can also be trained to carry messages,” the maester [Aemon] went on, “though the raven is a stronger flyer, larger, bolder, far more clever, better able to defend itself against hawks ...
- Continuing this idea to flying to Dragonstone. It's about the same distance from Winterfell to Kings Landing as it is to Dragonstone. The show claims it to be about 1000 miles from Winterfell to King's Landing (according to the user). This gives us about 3 days of raven flight if we take the 500 mile per day cap set by the users in the discussion above.
- Dany and her dragons likely took around 8 or so hours to fly to "Snow team 6"
- The user approximated around 125mph for a Dragon with a rider. Given the size of the Dragons, this seem possible as a normal hawk is able to fly around 70mph. Whether wingspan changes speed is unclear but big birds tend to be quicker than small birds.
This gives us about 5 days of total travel from Gendry running to the Dragons arriving.
The ice aspect is a bit strange. As 10˚F is around -12˚C and doesn't seem that cold for Gendry to be crying about the freezing cold weather. It was likely closer to -30˚C to -40˚C which I guess would make the ice freeze twice as quick. But bearing in mind that the Ice was thin in the first place there might be something that was preventing the water from garnering thickness very quickly. Such as the hot springs which exist naturally in the north (Winterfell's walls, Ygritte and Jon's cave) may have slowed the freezing of the water.
There are theories it can be done in ~3 days.
If we take the 500 miles per day, and the fact that white Ravens can fly from Old Town to Winterfell, it's possible a Raven can fly to Dragonstone from Eastwatch directly. This would cut down travel time to about 2 days of raven flight (at 50mph with rest). If we take a Dragons airspeed to be around 200mph it would do the return flight in 5 hours. Easily done in ~three days, allowing for better calculation for the rate of freezing of the water.