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?