I flew solo at about 10 or 11 hours. My instructor and I used up too much of the block for the dual practice so when I went up for my first take-off and landing I only had a short time until the plane was supposed to be back for the next student. The tradition, or so I'm told, is to do 3 T&Gs, but I only did one so I could get the aircraft back. Looking back I wish I would have done three, they would have gotten over it.
Incidentally, the shirt-tail thing is from the days when most trainers were tandem, like the old T-6s. The instructor would pull on the shirt tail when he wanted to yell in the students ear. When the student soloed he no longer needed the shirt tail for his instructor to tug on so they cut it off. Now we usually use a T-shirt that the student wears and I usually cut off most of the back of it and right all the pertinent info on it.
Don't sweat the time. do your best, enjoy the experience. if it goes beyond 20-25 hours there should be a reason. i.e. busy airspace, problems in some areas, weather, frequency, tentative instructor. But don't overanalyze.
it's about one of the best feelings there is.