The distance between Kyoto and Fukuoka is 322 miles as the crow flies. According to Google Maps, you could make the drive in a little under 8 hours, or you can take the Shinkansen and get there in 3.5 hours. We decided on the high speed (200 mph top speed) futuristic train.
With all the time saved by riding a bullet train, we had a flexible day, so we stopped in Kobe for lunch and Hiroshima for dinner, making a quick trip to Itsukushima for World Heritage Sites and deer!
We arrived in Fukuoka that evening for the last leg of our trip.