So Murph solved the equation before Cooper even ejected himself into the blackhole?
I just noticed something. Before they use the blackhole as a sling shot, Murph and Cooper are about the same age biologically. The slingshot cost them like another 50+ years. (58 if I remember correct). So Cooper is theoretically 120 years, while Murph is already a grand grandma by the point Cooper is about to eject himself.
I guess everyone understood how the Tesseract works. Cooper was practically the ghost, giving himself codes from the future. Cooper giving Murph the code was inevitable by this point. She collected the wristwatch from her old room and realized what was going on with its second hand. Murph was still about Coopers age at this point = Real Life Cooper still is about to sling shot around the black hole, while Blackhole cooper is already giving her the quantum data (58 years earlier than he actually slingshots himself).
So in summary what I try to say is, by the point the endurance circles around the blackhole, murph already solved the gravity problem and the Cooper Station was already orbiting Saturn. The world was saved before Cooper realized it himself and entered the blackhole.