Hi Kari,
Disney's Race for the Taste is scheduled for Sunday October 11, 2009 from 7am to 9am. The race offers two courses, the 10K, which begins at Disney's Wide World of Sports Complex and takes participants through a portion of Hollywood Studios, past the Boardwalk Resort area, with a finish at Epcot. The 3K race begins and ends at Epcot. You can see a map of the race as well as additional race information
here.
While the race does end about the time Epcot is opening, the race participants do have additional activities they can join in at Epcot. Therefore you will most likely find heavier crowds throughout the day at the park. On top of the race, it is also a scheduled weekend of Epcot's Food and Wine Festival, which is extremely popular and typically brings in large crowds for the amazing food, drinks and events.
If you are not a race participants and you are hoping to skip some of the race crowds, I like to use
www.touringplans.com to help decide which park to visit daily. The site uses a series of information like past crowds, holidays and special events to rate the expected crowd level at each park on any given date. The park crowds for that weekend are in the higher end (an eight out of 10) but the suggested park to attend on race day is Animal Kingdom. Sundays are usually a slower day at this park, and with the race pulling a great number of guests towards Epcot and Hollywood Studios, you should find the crowds at Animal Kingdom manageable.
Hope you have a great time!