Not any longer than if there is a return address, assuming postage is applied.

Lack of return address has no bearing. How long delivery takes depends largely on distance from the destination.

The same amount of time as a letter with a return address.

Depends on where its being posted from, and we're its being posted to. Some places, it only takes a day or two from when the letter is picked up to when its with the mail carrier ready for delivery. The uk show top gear did an episode where thry raced a letter posted at the bottom of the country all the way to the most northerly point, driving pretty much continously from one end of the country to the other. It took them less than a day, and the letter still got there first. On the other hand, posting a letter from sone mountain village in nepal to some other remote part of the world might take weeks.