Been in ever N.P. west of Smokey Mountains and it is real easy to be 20 miles away from another person in some, its not that hard to be twice that far in many.
Just got back from a Nevada trip, where probably 95% of the state is various forms of federal (BLM, NFS, or whatever). And there were some of the days when we could literally drive for hours on dirt roads, and never see another vehicle or person.