it took 31 days for Joy Rainey to drive from the Pacific to the Atlantic (Los Angeles to Daytona Beach) in a 1904 Curved Dash Oldsmobile

http://joy-across-america.com/journey-blog/ for her story in her own words

For the basic story http://www.washingtonpost.com/cars/would-you-drive-a-109-year-old-oldsmobile-across-the-united-states/2012/08/09/3b4f7316-e253-11e1-89f7-76e23a982d06_story.html