My friend is at ft lee he is going to fail all his pt tests he totally lost himself how long until they start his chaper paperwork?

The sad part about this question is, not so much that the young soldier wants out, but the whole attitude behind it. Attitude. character, and determination are developed when you're young and in the military, if you've joined and are carried on thru out your adult life. If this young man is quitting because things are hard or appear that way...can you imagine what he'll be life when "real-life" hits him in the face? It's not like he's away from his "mommy & daddy," he's either a Reservist or Guardsman (no ding against the AR or NG...I've been both) and is in training and sees them every evening. His parents need to cut the apron string, and let the young man grow a pair of b*lls...I say keep him in and motivate him to complete his "commitment" to our country.

Realistically - Unless he was never 'in-shape', it should only take a about a month (6-7 weeks if not) to get his-self toned up and ready to go. Here's a regiment of exercise he can follow that will return him to a decent physical attitude within a short period of time.
These should be done 3 times a day, every day. They can be done in PT, Duty or Civilian attire, including the weekends.
Week 1 -
1. Start at the basic 50 push-ups as fast as he can. (when he's done stop and turn over to number 2 below) Don't worry about form but about speed - Correct form will follow since that is actually the easiest way for a human male body to do push-ups. The reason why 'female' push-ups were designed the way they are is to allow for their body form.
2. Do the basic 50 sit-ups, as fast a possible. Again don't worry about form but about speed. (when he's done stop and immediately do number 3 below)
3. Immediately hop up on a hanging bar and do 3 pull-ups (hand palms away from you). Drop then climb back and do 6 chin-ups (hand palms towards you from you). (when he's done stop, then do about 3 minutes of limbering up his muscles by doing 25 jumping jacks and 25 windmills (take a 2 minute break in the shade - do number 4 below BUT every other day in the evening - NOT after each exercise period)
4. Go to a track or marked course
Day 1 and 2: Run a 3/4 mile (3 laps) as fast as he can.
Day 3 and 4: Run 1.5 mile (6 laps)
Day 5: Run 2.5 miles (10 laps)
Day 6: No Running - just the exercise regiment described above .
Day 7: On a track or a marked course - run. Don't worry about time but start the first half-mile at a moderate pace to loosen-up, pick the pace up but don't strain his-self during the middle mile. The last half-mile (laps 7 and 8 on a standard track) he should begin to do open-mouth breathing to bring air into his lungs for the final push. After he in the last half-lap of lap 8 he should start to swing his arms and extend his stride. The last 50 yard stretch, he should use his toes to lift his body-carriage so he can splint (its probably gonna be ugly to watch him since he's tired - but that will be the least of his worries), swinging his arms and hauling ass.
Once he crosses the finish he should walk it off and get to the shade while he cools down
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Additional advice:
After Week One, the amount of exercises should be raised by 10.
The next week 10 more,
And so and so on...
Somewhere in here he will peak and his mind will tell his body he can't do it.
That's when he needs to push through it and finish anyway.
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Other people will tell you lots of things but I'm 64 and that's the same regiment I used for 20 years in the Army and prior to every time I deployed as a civilian contractor.
It also works if you've been deployed and need to get back in shape after a long time gone. Sometimes there is no 'PT' other than humping your gear day after day.
I tend to stick to the practical advice and leave all the physiology discussions of why to the college PhD fellows
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If he's fading out sometimes the only way to 'Get over the Hump' is to 'Stay the Course'.
Hope this helps.

If his/her plan is to intentionally fail their PT test in order to get chaptered out I hope they jerk his/her chain for a good long time and give them every lousy detail until they are out. If I don't have a grasp of all the circumstances because you haven't given them and there's more to the story than let's here it, otherwise why did this individual enlist in the first place? My understanding is that they will probably get a General discharge and bar to reenlisting, a General may hurt them in the future for jobs etc. Personally I think they should give such folks a Dishonorable discharge but I don't make those decisions.