When my father had a heart attack, I was told to drive to the hospital, which was a ~10 minute drive (at the speed limit). Another family member called the hospital to let them know we were coming.

During this drive, the speed limit mattered very little to me, and I drove as fast as I possibly could.

Whether this was "right" or "wrong" isn't something that crossed my mind at the time. When one's own life (or the life of a loved one) is on the line, people have a tendency to do things that don't make sense to an outside observer.

Luckily for us, we arrived at the hospital without further incident, and my father was quickly cared for. I didn't time the trip, but I imagine it was only marginally faster than driving at the speed limit, as my vehicle at the time wasn't particularly fast.