running a GS

Question
We just adopted a 1 1/2 year old GS and malamute cross named Simba. He
had not had enough food, affection, exercise or discipline from his previous
owners. After just over a week he's doing much better - he is starting to put
on weight, heels properly (meaning he considers us his pack leaders) and is
even getting along with our two cats - previously the queens of our nest. My
question is about exercise. With the approval of our vet we are running Simba
next to our car with a leash almost every day. Taking a walk, which we are
also doing, just isn't getting those ants out of his pants. We're up to 3 1/2
miles now. First off, how far could or would a GS want to run in one day if he
or she were not limited? We'd like to really tire him out but not push him too
hard. Even if we think we've given him a good run he still seems to have too
much energy when we bring him home. Also, the second part of my question
is, how do you recommend we train him to use the treadmill? We'd have one
but have not tried it yet because I am afraid he will have a bad experience on
it and that will turn him off running on it. I've seen dogs using treadmills and
for dog owners like us, who live where it is cold and snowy, a treadmill would
be a great answer for days that are just too icky to take a long walk/run.
Thanks for any help you can give me.

Answer
Even if the vet said it is OK, I still think 1 1/2 years old is a little young to be running with a car.  Perhaps a good game of fetch in the back yard would be easier on him.  

I am not sure how to train on the tread mill.  I guess use praise and treats to encourage him.