Over 100 miles of Greenway trails in Knox county. Third Creek is 5.3 miles but connects to other Greenway. http://www.outdoorknoxville.com/places/greenways http://knoxvilletn.gov/government/city_departments_offices/parks_and_recreation/greenways_trails
Look up the course route for the Knoxville Track Club's Cross Knox 15k. It's almost 10 miles of all Greenway from Morningside Park to Bearden. The route will go even longer if you are willing to run on a few sidewalks or the path through Cherokee Blvd.
You can go 6.5 out to james white parkway all on greenways. The trails are on google maps bicycle layer
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