Flight Haneda Airport departs from Tokyo Haneda Airport at 10:15 and arrives at Fukuoka Fukuoka Airport at 12:10.
The flighttime is about 1h 55m. The distance travelled ("as the bird flies"): 1048 Km. So the average speed is roughly 547 Km.
The best day to arrive at Tokyo is Sunday and it would be best to avoid Wednesday, as prices are on average 178.13% higher than on Sunday. (Average prices, based on 3353589 datapoints.)
We have a lot more statistics for flights NH 249 and between Tokyo and Fukuoka.
