I privately wrote a longer and little more complete reply to the original
poster, since it's pretty marginal with endurance, but I just wanted to make
this point to the group:
>As yes, I will certainly consider worthy candidates from the shelters...but
>a greyhound sounds like a breed that could "keep up".
These guys run 35-45 miles per hour for a mile or so, then drop down to 
15-20 mph for a little longer.  I doubt you could find them 5 mins after 
you started your ride, unless you rode with them on a leash, and that's 
probably not what you had in mind.
I would be happy to discuss this thru private email, or you can check out
rec.pets.dogs.
Rosalie