(1) Your weekly mileage/running time amount is more important than your longest run. Basically, for the average runner, you can do a comfortable Half if your weekly mileage (thus, corresponding running time amount)for the past two weeks has been in the 24 - 26 miles per week range. Basically, your comfortable race running distance when you go into the Half marathon race distance is 1/2 of your weekly mileage. If you have run 3 8 milers in the week before your 9 miler (giving you a minimum of 24 miles for the week assuming that you are running endurance distance every other day irrespective of the track speed work on one of the endurance "off days"), then you ran a minimum of 24 miles for the week. This tells me that you are solidly based for a possible comfortable Half marathon race. However, if you have not reached the 24 - 26 miles per week of endurance running plus at least one session a week on the track for speed work, you are not well prepared for a Half marathon race debut.
(2) That being said, you could sign up for the Half race but, if at mile 9 or 10 you begin to feel quad fatigue (which is the main thing that will make the running uncomfortable), take it to a walk. I say this because there is no sense in messing up your training schedule by putting yourself into a week or two week recovery if you overpush the "earlier" Half race run.
(3) If you want to have a really enjoyable and satisfying first Half Marathon race, get you mileage up to 30 miles a week which will include an 8 miler one day, rest, then a 9 miler, rest, and then a 10 miler followed by a session of speed work on the track two days after the 10 miler.
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