Cats have been known to travel large distances just to get back home.  I
don't think it's unlikely that he's traveling this far in search of food.
My sister had a cat who would not stay put no matter what and it wasn't
unusual for her to get calls from people telling her they had seen him two
miles away at the golf course.

It's too bad you or your brother can't convince him to stay put and make one
of your places a permanent home.

Celeste

I don't know if cats' ranges have ever been formally studied but there are
certainly some interesting anecdotal stories.

For instance, I've heard that the old Disney film The Incredible Journey is
based on a novel which was based on a true story, though I can't find any
clear statement of that in a Google search I just did. In the movie, two
dogs and a cat journey something like 250 miles through wilderness to get
back to their owners.

I saw a documentary a few years back that explored the case of a cat who
went a rather substantial distance in England. Its family had moved at least
100 miles, maybe twice that (I don't recall for sure), taking the cat with
it. The nearly full grown daughter had stayed behind in the old home for
some reason (to go to school perhaps?) Shortly after arriving at the new
home, the cat disappeared and no amount of searching could locate it.
Several weeks later, the cat showed up at its old home where it was
discovered by the daughter (or neighbours living close to the old home). The
cat had walked at least 100 miles and had _not_ gone in a straight line
because there was a major river between the new home and the old one, which
forced the cat to make a major detour to bypass the river.

I imagine that there are other such stories if you look for them.

Your situation is interesting because the cat has covered 3 miles in half a
day; I'm not sure if that is credible or not. It seems a longish way to go
in just a few hours. But it seems like it might be possible. I don't suppose
there's any possibility of putting some kind of tracking device on the cat
to follow it? Or maybe you could put a recognizable collar on it or tie a
scarf around its neck or something so that you could be certain that it was
the same cat?

Rhino

Males can have a range of 10 square kilometers- female ranges are usually a
lot smaller.