Only 83 days at warp 6.2, the standard cruising speed for an Intrepid-class starship (or 7.13 days at warp 9.975, maximum sustainable speed for the same ship).
https://setiathome.berkeley.edu/forum_thread.php?id=34381#:~....
100 ly in 7.13 days would’ve had them home in 13.6 years even without shenanigans. (The warp speed graph I saw suggested more like 7 years, which is even worse for the fundamental plot contrivance of the show).