Fix it the right way not the wrong way.
How to fix split door hinge.
Apply petroleum jelly to the movable portions of the hinge to protect them from the glue.
Then scuff the cup portion of the hinge with sandpaper where it will contact the adhesive.
If you have a centering hinge drill use the hinge as a template and the finish repair will be better than new and last for years.
I m thinking the best way to fix this short of ripping out the whole door frame would be to drill out the split wood chisel it square then glue in a new piece of wood for the hinge to be screwed into.
Another hint is to use a long screw in one of the holes in the top most hinge long enough to penetrate the stud.
In most cases if the door rubs on the jamb or the floor it can be repaired by attending to the hinges.
Place the door across two sawhorses.
Start by removing the hinge from the door and preparing the damaged area photo 1.
The wrong way is a temporary fix not cool.
Remove the door from the jamb using a drill driver.
The top hinge on one door has come away from the door frame the wood is split and soft so the screws have no bite.
How to fix a door that cracked where the hinges go 1.
After time the weight of the door will pull on the hinge and cause the door not to hang straight.