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I can't answer this question because I know that Harry lives in Surrey, but I don't know where Hermione or Ron live? Do you know?

And even if you do not know, do you have any idea how much time Hedwig takes to bring a letter?

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    Hedwig, like most space vessels, flies at the speed of plot. – EvilSnack Aug 12 '18 at 20:52
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tl;dr: Most likely within mere hours.


While we do not know exactly where either Ron or Hermione live [we have actually no idea at all about Hermione], nor where in Surrey Little Whinging is supposed to be, we do know a couple of things:

  • Hagrid drops Harry of at Paddington for his return to Little Whinging after the shopping trip on his 11th birthday. [PS]

  • Errol managed to get Molly's Howler from The Burrow to Hogwarts between Dumbledore writing her and Arthur about the boys arriving by car (which he could have done after the feast he had to return to at the earliest) until breakfast the next day. Meaning a school owl had to deliver Dumbledore's letter, Molly had to write down her answer and then had to send her old bird across the country. [CoS]

  • The Burrow can not be too far from London, because Muggle taxi drivers where willing to drive 9 (all the Weasleys except Arthur and Percy plus Harry and Hermione) people to King's Cross. I don't know how this works in the UK, but I expect that they could not be long distance trips (because otherwise either taking the Knight Bus or flooing to the Leaky Cauldron and taking the Tube to the train station would have been cheaper and much quicker). [GoF]

  • The Burrow is somewhere to the west of Little Whinging, but not too far west (the Wiki states Ottery St. Catchpole is in Devon but gives no proof [but based on the guess that it might be near the River Otter in Devon]), meaning either to the south west or the north west of Surrey:

You’re driving too far west, Fred,” [George] added, pointing at a compass on the dashboard. Fred twiddled the steering wheel. [CoS]

  • Hogwarts is in the Scottish Highlands.

At this point, it became a matter of urgency to find some more discreet method of transporting hundreds of wizarding children from all over Britain to their secret school in the Highlands of Scotland. JKR on Pottermore "The Hogwarts Express"

  • Bird of Prey Flight Top speeds in the Real world - it is uncertain if those are the same in the magical world. Pigwidgeon - when he did not yet have a name - was able to keep up with the Hogwarts Express for at least a bit, so maybe magical owls are faster. Barn Owl 50 mph Snowy Owl 50 mph Great Horned Owl 40 mph Short-eared Owl 26 mph

Conclusion: If Errol of all owls can get a letter overnight from most likely Devon to the Highlands of Scotland, Hedwig will be quicker to deliver a letter from Privet Drive to either The Burrow or almost anywhere else on the island, so wherever Hermione may live it would most likely be nearer to Surrey than Hogwarts. In fact, the answer of a letter from Harry to either of them should reach him within hours.

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    While it is not required by the question it would be interesting also to learn what might have been the average speed of an owl, both considering it simply flies the whole way without stops and also with some biology checking , regarding how far owls usually can fly without rest. – Gnudiff Aug 12 '18 at 14:53
  • @Gnudiff A agree, but all I have is my Harry Potter books, and owl speed - apart from the fact that the as of then not yet named Pig managed to keep level with the Hogwarts Express at least long enough for Harry to snatch him up in PoA - is not mentioned (with the possible exception that tiny owls should be used for local deliveries only) in them, I couldn't say anything about that. But I found some info and will add it now--- – BMWurm Aug 12 '18 at 15:00
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    @brt22 Cool. Like I said the Potter wiki says Devon as well, but - to me at least - there is Pottermore and Written-by-JKR-Pottermore. The first is the staff there inventing stuff (that hopefully does not contradict existing canon), the second is word-of-god. But Devon is a fairly good guess, since the River Otter is located there, as well as the real village of Ottery St. Mary. – BMWurm Aug 12 '18 at 15:30
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    @BMWurm You’d expect so, wouldn’t you? I doubt Umbridge has everything staged, though: the letter is signed by Mafalda Hopkirk (as was the letter in CoS), and Umbridge never told anyone she was the one who sent the Dementors. I think owl speed is a somewhat inconsistently described deus ex machina, similar to the Fidelius Charm. On the one hand, there are the almost immediate ones from the Ministry; on the other, there are the letters from Sirius while he’s in hiding, which take several weeks to arrive. It doesn’t seem like Rowling has given much thought to owl speed overall. – Janus Bahs Jacquet Aug 12 '18 at 15:57
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    @JanusBahsJacquet Essentially owls travel with the speed of plot - (Warning TV-Tropes! tvtropes.org/pmwiki/pmwiki.php/Main/TravelingAtTheSpeedOfPlot – BMWurm Aug 12 '18 at 19:28
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There is contradictory evidence

In the beginning of Goblet of Fire there is owl correspondence between Harry and Ron.

Harry — DAD GOT THE TICKETS — Ireland versus Bulgaria, Monday night. Mum’s writing to the Muggles to ask you to stay. They might already have the letter,

I don’t know how fast Muggle post is. Thought I’d send this with Pig anyway.

We see here that Ron is not sure whether owl post or Muggle post is faster. It is clear that he did not write his letter after his mother did, and presumably he sent the letter when he finished writing it, but it is possible that his mother didn't mail the letter right away. Even assuming that both letters were sent at approximately the same time, they arrived at Harry's house at about the same time as well so it would appear that owl post is just as slow as Muggle post.

However, Harry responds right back to Ron:

Harry seized his eagle-feather quill once more, grabbed a fresh piece of parchment, and wrote:

Ron, it’s all okay, the Muggles say I can come. See you five o’clock tomorrow. Can’t wait.

Harry

This appears to assume that Hedwig would be able to deliver the letter in one day, which is probably faster than Muggle post.

We also know that Hedwig is pretty fast because in the beginning of Prisoner of Azkaban she got to the Leaky Caulldron only five minutes after Harry did via the Knight Bus:

“Very smart owl you’ve got there,” chuckled Tom. “Arrived about five minutes after you did. If there’s anything you need, Mr. Potter, don’t hesitate to ask.”

On the other hand, there are times when it takes Hedwig very long to deliver mail, especially to/from Sirius. When waiting for Sirius's reply to the letter about Harry's scar pain, we find the following:

“But we don’t know where Sirius is ... he could be in Africa or somewhere, couldn’t he?” said Hermione reasonably. “Hedwig’s not going to manage that journey in a few days.”

This indicates that it is unreasonable to expect Hedwig to be able to fly to Africa in a few days. A few days later we find:

“It’s been over a week,” Harry said, looking at Hedwig’s deserted perch. “Ron, you don’t reckon Sirius has been caught, do you?”

This already implies that it is kind of expected for Hedwig to be able to fly both ways (to Africa, or even further) in about a week.

Hedwig didn't actually return for another four days after that, on Thursday night1 while they were doing their Divination homework:

“Hedwig!” he shouted, and he launched himself out of his chair and across the room to pull open the window.

When Harry does get Sirius's reply he sends a letter right back. At this point Sirius is already on his way to the Hogwarts area, so we would expect Hedwig's journeys to be shorter. Yet Harry doesn't receive Sirius's next response until October 30, which is about a month and a half later:

When they went down to breakfast on the morning of the thirtieth of October, they found that the Great Hall had been decorated overnight.

There is no particular reason to think that Sirius took an especially long time to write the letter; in fact, the letter appears to be just a quick reply:

Nice try, Harry.

I’m back in the country and well hidden. I want you to keep me posted on everything that’s going on at Hog warts. Don’t use Hedwig, keep changing owls, and don’t worry about me, just watch out for yourself. Don’t forget what I said about your scar.

Sirius

Harry sends another letter to Sirius after his nighttime adventure with the egg, and it again takes a month for him to get Sirius's reply. This can be derived as follows: Harry goes to Hogsmeade halfway through January:

There was a Hogsmeade visit halfway through January. Hermione was very surprised that Harry was going to go.

After running into Rita Skeeter in Hogsmeade they go visit Hagrid. While there Dumbledore says:

“I refuse to accept your resignation, Hagrid, and I expect you back at work on Monday,” he said. “You will join me for breakfast at eight-thirty in the Great Hall. No excuses. Good afternoon to you all.”

After visiting Hagrid, Harry decides that it is time to take Cedric's advice:

Lying to Hagrid wasn’t quite like lying to anyone else. Harry went back to the castle later that afternoon with Ron and Hermione, unable to banish the image of the happy expression on Hagrid’s whiskery face as he had imagined Harry winning the tournament. The incomprehensible egg weighed more heavily than ever on Harry’s conscience that evening, and by the time he had got into bed, he had made up his mind — it was time to shelve his pride and see if Cedric’s hint was worth anything.

We are then told when Harry went on his excursion:

On Thursday night, Harry sneaked up to bed, put on the cloak, crept back downstairs, and, just as he had done on the night when Hagrid had shown him the dragons, waited for the portrait hole to open.

Thus, this occurred almost a week after the Hogsmeade visit which was halfway through January. The next day, which would be Friday, Harry told Ron and Hermione about the previous night's adventure:

Harry had been recounting his adventures of the previous night in whispered installments for the last half hour.

Then we are told that Harry sent an owl to Sirius that night:

Obedient to Sirius’s wish of hearing about anything odd at Hogwarts, Harry sent him a letter by brown owl that night, explaining all about Mr. Crouch breaking into Snape’s office, and Moody and Snape’s conversation.

This means that Harry sent the owl on Friday night, one week after "halfway through January". So we're looking at somewhere around the 21st of January. Sirius's reply arrives on February 22nd:

Just as it had before he faced the Horntail, time was slipping away as though somebody had bewitched the clocks to go extra-fast. There was a week to go before February the twenty-fourth (there was still time) ... there were five days to go (he was bound to find something soon) ... three days to go (please let me find something . . . please) . . .

With two days left, Harry started to go off food again. The only good thing about breakfast on Monday was the return of the brown owl he had sent to Sirius. He pulled off the parchment, unrolled it, and saw the shortest letter Sirius had ever written to him.

Thus, it took a month for the owl to get to Sirius and back. Again, while it is possible that Sirius just waited a few weeks to write his reply, there is no particular reason why he would not write back as soon as possible, especially considering that his reply was to ask them when they would next be in Hogsmeade (if he delays replying he might miss the date).

However, the next exchange takes much less time. Harry responds immediately (Monday, February 22nd as per above) noting that the next Hogsmeade visit is the weekend after next. That would make it Saturday March 6th (assuming it was not a leap year – the actual year 1995 was not, but the days of the week in the book do not match the actual year of 1995, so who knows). Sirius's reply comes one day before that:

The brown owl that Harry had sent to Sirius with the dates of the Hogsmeade weekend turned up at breakfast on Friday morning with half its feathers sticking up the wrong way;

Thus, this exchange took only half as long as the previous one (February 22nd – March 5th).

After Visiting Sirius in Hogsmeade Harry sent a letter to Percy, and he didn't get the response for well over a month. This can be derived as follows: The Hogsmeade visit was on Saturday March 6th, and they sent the letter to Percy the next day:

Harry, Ron, and Hermione went up to the Owlery after breakfast on Sunday to send a letter to Percy, asking, as Sirius had suggested, whether he had seen Mr. Crouch lately.

Percy's reply didn't come until sometime in mid-April:

Hedwig didn’t return until the end of the Easter holidays.

Here it is more believable that Percy would have delayed responding, but it still took well over a month. On the other hand, the very day after sending Hedwig to Percy we find:

When the post owls arrived, Hermione looked up eagerly; she seemed to be expecting something.

“Percy won’t’ve had time to answer yet,” said Ron. “We only sent Hedwig yesterday.”

This indicates that it is pretty obvious that Hedwig can't make it to the Burrow and back in one day, but on the other hand, it is not so far out of the realm of possibility that Ron would never even suspect that Hermione thought that Percy's reply could have arrived.

After the incident with Mr. Crouch, Harry has another exchange with Sirius, but this time it only takes one day:

Sirius sent their owl back the very next morning.

Clearly, it is possible for an owl to get to the mountain cave by Hogsmeade and back within one day (which is eminently reasonable, as Hogsmeade is within walking distance of Hogwarts).

In short, from the above few examples there already seems to be contradictory information about how long it takes Hedwig (and other owls) to travel. This is likely because JK Rowling did not put that much thought into making sure that all the owl journeys were consistent. Alternatively, the long waits for responses from Sirius is a plot device, and the author didn't care that it doesn't match how long the journeys should actually take.


Notes

1. There is actually an inconsistency here. The "it's been over a week" comment occurred on Sunday:

“It’s been an absolute uproar,” Percy told them importantly the Sunday evening before they were due to return to Hogwarts.

The Hogwarts Express leaves the next day, which is Monday:

There was a definite end-of-the-holidays gloom in the air when Harry awoke next morning. Heavy rain was still splattering against the window as he got dressed in jeans and a sweatshirt; they would change into their school robes on the Hogwarts Express.

The first day of classes would then be Tuesday. Fred and George discuss their experience in Moody's class that evening at dinner:

No sooner had she gone than her seat was taken by Fred Weasley.

“Moody!” he said. “How cool is he?”

“Beyond cool,” said George, sitting down opposite Fred.

“Supercool,” said the twins’ best friend, Lee Jordan, sliding into the seat beside George. “We had him this afternoon,” he told Harry and Ron.

We then find out that Harry doesn't have Moody until Thursday, which should be two days later:

Ron dived into his bag for his schedule. “We haven’t got him till Thursday!” he said in a disappointed voice.

Yet their first class seems to have not occurred two days later on Thursday:

The next two days passed without great incident, unless you counted Neville melting his sixth cauldron in Potions.

Yet when they do have the class the next day (which should be Friday) it is still Thursday:

The Gryffindor fourth years were looking forward to Moody’s first lesson so much that they arrived early on Thursday lunchtime and queued up outside his classroom before the bell had even rung.

Thus, when Hedwig returned while they were doing their Divination homework the night of the day when they had Moody's first class, it should have been Friday five days later but according to the book it is Thursday (and thus only four days later).

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    I don’t think the correspondence with Sirius provides very good evidence that the evidence is “contradictory” as you say. There are dozens of reasons why Sirius may not rely immediately, or may intentionally make it seem to take longer to reply. Regardless if the letters he returns are short, you’ve made a rather big assumption on Sirius’ reply speed when no such evidence exists. As the youth of today might say “maybe he just left Harry on read.” – Edlothiad Aug 12 '18 at 19:07
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    @Edlothiad Plus with Sirius travelling - probably mostly in dog form - Hedwig might have trouble finding him until he turns human again... – BMWurm Aug 12 '18 at 19:24
  • Just a note: 1 September when the Hogwarts train leaves is always a Sunday, and classes always start the following day, on a Monday. The Percy quote must be a mistake by Rowling; it should have read ‘Saturday’ for the rest of the calendar to make sense. – Janus Bahs Jacquet Aug 12 '18 at 19:35
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    1 September is always a Sunday? Do the magicals have a different calendar? – QuestionAuthority Aug 13 '18 at 5:58
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At the start of Prisoner of Azkaban, Harry sends Hedwig off with a note for Ron, with instructions to keep herself away until Aunt Marge is gone. Aunt Marge stays for a week, and Hedwig reappears (presumably having delivered the note) the evening before Aunt Marge is due to depart, at the Leaky Cauldron where Harry has ended up.

Ron is at this point in Egypt. Google Maps says the distance from Surrey to Egypt is 2350 miles. To get there and back in a week, Hedwig will have had to fly at a steady 28mph all week with no stops for rest (or faster with rests). In incredible heat.

According to Environment Alaska, 30mph is towards the top end of flight speed for a snowy owl (they reach 50mph only when catching prey). Birds of North America says that during migrations snowy owls can cover 'hundreds of kilometers in a few days'. This trip is pushing it though, even for a snowy owl. Perhaps she stowed away on a plane? She is a very clever bird.

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    "Ron is at this point in Egypt": Do you have a quote to back this up that you can edit in? And "they reach 50mph only when catching prey" would mean they should easily be able to do 50mph without holding prey. Also of note is: magic! – TheLethalCarrot Feb 12 at 14:25

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