Possibly, but I personally wouldn't chance it. Here is a training program for 9 weeks that includes beginners, but this is how they define beginner. .. "Beginner Profile You've run for at least a year, but you're still a racing neophyte.
You can run 5 miles at a time without distress, average 15 to 20 miles a week, and have finished a 5-K, perhaps even a 10-K. Now you want to go longer, though not yet to a marathon, and your race time is less important to you than finishing. " runnersworld.com/article/0,7120,s6-238-2... As you can see training or Half Marathon takes quite a bit of ramp up even for seasoned runners.
Yes a friend of mine did a half marathon and trained for about 6-8 weeks only. What they did was for a team corporate event so every lunchtime they did a medium run, about 30-40 mins and then twice a week she would do longer runs around her home area, adding 200-500 meters each time and changing the run from down hill to up hill etc. She got very good very quickly but she did put in 110%. Training schedules should be based on what YOU can do and how far YOU want to stretch yourself.
Work backwards! Write out the training schedule with you doing a half marathon ( or close to it ) a week before the big race ( no sooner because you need to carb up for the week prior to the event. The week before that take off some distance and work out with Google Maps how far that is around your area and see what that entails.
The week before that, take off some of the distance and do the same thing. So if your training for this event you should have a good three weeks of build up to a good distance, each day or second day adding more distance and strength ( up hill!). The first 3 weeks will be you getting used to running and getting better at judging how long it takes to run a certain distance..... My best tip from her was how much she pushed herself in the last few weeks - by then she was a bit tougher and could really give it everything.....and working out routes around her home so she knew exactly how far the run was going to be.....she did well if I remember correctly :).
Disclaimer: I've never trained for anything longer than a 10k, have never run farther than 10 miles. At age 25, slightly overweight, never having run any significant difference before, I trained for a 5k in less than three weeks. Not a fast 5k, mind you (10 minute miles), but I finished the training and race without injuring myself (though, due to my inexperience, that was partly luck and partly resilience of a 25 year old body).
The thing is, everybody's bodies have differences. 10-12 weeks sounds right to me for an average person who can dedicate themselves to a program to train for a half-marathon -- a mile a week really isn't too much to add. But you might be able to do it much sooner: I've had friends who've walked out the door to go running for the first time and comfortably done 3-4 miles.
I knew a guy who, not having trained on more than the occasional 5 or 6 miles, decided on a lark to run a Marathon with his girlfriend and made it 20 miles (not recommended). You might also have more trouble -- some people are not built well for running. So my own suggestion would be to gently train for a week or two or three and *then* gauge yourself.
If you float into running three miles the first day, I suspect a somewhat competetive half-marathon is within your reach in six weeks. If you find your first mile is hard, or you find yourself hurting (especially in your joints), you'll want to take it slow, possibly even slower than twelve weeks. In this respect, I guess I'm just mostly echoing the advice of others: train for a smaller distance (5K is great) first.
It will give you a great idea of the strengths and weaknesses of your own body and help you learn how to train around them. OK - follow bibbit's Higdon program, that looks good. Given your age and weight, it shouldn't take you long to get up to running three miles.
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