How long should video clips be to be in sync with a 90 BPM song?
If you want a new image at every beat, start with the frame rate of your video. 30 frames per second gives 1800 frames per minute. Divide that by 90 to get the number of frames per beat, in this case 20. So if you change the image every 20 frames the pace will be the same. You do have to align the cuts with the beat; just matching the pace is only part of the battle.

In the general case:

(FPS x 60) / BPM = number of frames per beat