Province Size?

[tinkthank]

How big are provinces?
I am trying to imagine this and am having problems. On the one hand, a province must be large enough to encompass at least one decent size town and take a troop of, say, 20 one month to move through it. On the other hand, it must be small enough so that a province defence of, say, 10-20 men can patrol it and automatically meet any force moving in; it must be small enough so that an invading army of, say, 10-20 men automatically meet up with some defending force of, say, 10-20 men on some field.
This seems incompatible. But I want to try to figure it out.
I think provinces which are portrayed in the �world� map are much too large � a PD of 3 can never patrol an area the size of Wales � or Texas � and hope to meet up with anything. What are the chances of you successfully finding a friend with whom you agree to meet �next Thursday� in �New York City�, or �Chinatown�? You�ll never find her.
No, provinces have to be smaller.
But now let us imagine something like... some Alms somewhere between Unterammagau and Oberammagau. Unterammagau has a population of about 5,000, Oberammagau of about 15,000. It would be unlikely that a troop of 10 men would meet up with an enemy troop of 10 men on some alm there, but if you give them a month, it is sure to happen. Perhaps a patrolling PD force of 10 would have a chance of finding incoming strangers, given a month of time. Yet it takes about 1 to 1 and a half hours to walk between the two. Let�s say it would take 5 hours to walk if wearing full plate mail and carrying all your gear, that at a slow pace and looking for enemies hiding behind cows and trees and whatnot. But not a month. (Province type: Farmlands, Mountains.) In a month, even heavily armed troops can move from Texas to Nevada.
So it seems that a province is either too small to limit troop movement to anything under 10 and too large to give troops a snowball�s chance in hell of finding one another.
So what do you think?