Flight Haneda Airport departs from Tokyo Haneda Airport at 09:05 and arrives at Fukuoka Fukuoka Airport at 11:10.
The flighttime is about 2h 05m. The distance travelled ("as the bird flies"): 1048 Km. So the average speed is roughly 503 Km.
The best day to arrive at Tokyo is Sunday and it would be best to avoid Wednesday, as prices are on average 199.1% higher than on Sunday. (Average prices, based on 3280033 datapoints.)
We have a lot more statistics for flights JL 309 and between Tokyo and Fukuoka.
