My DH did the experience at WDW in 2003. He was in the morning session (Rookie Experience) & had to arrive at 7:30 am. The session got started around 8 am with instruction & then driving. The program end with the presention of certificates that include the drivers lap speeds. I'd say we were done by 12 pm or so.
The amount of time it takes for your DH will depend on the size of his class & the experiences. His was less than 10 drivers, of which 2 had the Kings experience. They do the ride-a-longs at the same time. Which I did & thought was a fun & fast!
While it took up the morning, we still had most of the day left to do as we wished.
PS -- Schedule the experience early in your stay, just in case it rains. On a prior visit, we scheduled it for our last day. When it rained, he had to reschedule. Luckily, we had a return trip planned. They will issue a raincheck that is good for 1 year & can be used at any of the tracks that have the Petty Experience.