Actually extra charges for National are based on 24-hour days from the pick-up time. National charges for 1 hour extra (dropped off more than one hour after the pick-up time but less than 120 minutes late). The hourly rate is usually one-half the daily rate, so being 2 or more hours late will cost an entire extra day.
With that said, dropping off 15 hours early will come up on the hand-held computer as the reserved number of days and you should simply be charged for the reserved time. In your case, if you had picked the car up at 11 AM, your tenth day starts at 11 AM on the ninth day and a drop off anytime after 1 PM on that day up until 12 noon on the next day should be charged the same (weekly plus 3 days, I assume).
The main time when you might have a problem with these bookings is when you are right between paying a daily rate for a multi-day rental and qualifying for a weekly rate. This should not be a problem with a 10-day rental.
I had an interesting problem with National a few years ago when I had just barely qualified for a "weekly" rate with a 4 day plus 3 hour booking (pick up scheduled for 10:30 am on Thursday, drop off scheduled for 1:30 pm on Monday). National's weekly rentals require a minimum 5-day stay and I was also using a weekly-rental discount coupon. This was January and we ended up iced in at O'Hare for most of Thursday, finally departing for MCO about 4 pm instead of our original 7:00 am departure. We picked up the car about 8 or 8:30 pm. Of course our return flight on Monday required check in at the airport by about 2 pm on Monday, so we planned to drop the car off as scheduled. We were using Counter (compact car, now I always use EA). Our "weekly" rental was now a 4-day rental and the rate to be charged was substantially higher (higher daily rate, no weekly discount coupon). I pleaded my case that I'd been stuck at the airport in Chicago for the better part of my first day of vacation, losing the benefit of all that fun in the sun and warmth of Florida and now I was having to pay even more for the pleasure because of the difference in weekly vs. daily rental rates. The National rep. at the counter played some magic with her computer and ending up dropping the daily rate to a level that made the total bill essentially the same as my original reservation quote. I left happy with the solution.
Ralph