Use of 'out' to indicate a particular distance from somewhere

Question

In Oxford Dictionary it has been shown that the word out can be used to mean situated far or at a particular distance from somewhere. It uses three phrases as example to explain this meaning. These three phrases are:

1. an old farmhouse right out in the middle of nowhere.
2. they lived eight miles out of town.
3. a cold front hundreds of miles out in the Atlantic.

I cannot understand the meaning of these phrase. Please help me.

One may think that I should make three different posts for these three phrases. I also thought to do it at first. But when I saw that these three phrases contain a common word out, and they are examples of a common usage of out to mean same kind of meaning, I have made only one thread.

Answer 1

1. An old farmhouse right out in the middle of nowhere (at a particular distance from somewhere).

It means an old farmhouse is located somewhere far away from any towns.

In the middle of nowhere means:

far away from any ​towns and ​cities and where few ​people ​live

[Cambridge Dictionaries Online]

2. They lived eight miles out of (eight miles away) from town.

It means the distance between the house where they lived and town was eight miles.

3. A cold front hundreds of miles out in (at somewhere in) the Atlantic.

It means a cold front is located in the Atlantic and it is hundreds of miles away from the shore.

Note: Out means (far) away in somewhere. It can be interpreted in various ways.

Answer 2

In this case, the word is being used as an adverb - it is modifying a verb. It is used to mean "away from the inside; not in or at a place, e.g. "Go out into the garden" (Definition from Chambers Dictionary)

an old farmhouse right out in the middle of nowhere.

Their farmhouse is far from the madding crowd - it is in a remote, rural location. The verb is implicit, and is "is". In full, the sentence would be "They live in an old farmhouse which is out in the middle of nowhere."

they lived eight miles out of town.

lived is the verb here.They live at a distance of 8 miles from the town.

a cold front hundreds of miles out in the Atlantic.

The cold front is hundreds of miles off of the coast, or hundreds of miles away from the coast. This is again like example 1), "There is a cold front which is hundreds of miles out in the Atlantic."