My wife drives a 2005 Mazda 3 with about 25k on it, and she absolutely adores it. She parks it in our “garagement” (you know, where the garage is part of the basement). Basically, the driveway is about 20-25 feet long, and descends from ground level to basement level over that distance, so it’s fairly steep. Anyway, the wife drives in nose first into the garagement, meaning she has to back out up the hill to leave. She insists the best way to get out is to hammer it as fast as possible, because the time duration is less. I think she should do it as slowly as possible to reduce the force on the reverse gear. Plus, I can hear the transmission wining when she does it, but it doesn’t when I do it slowly. She’s already killed one reverse gear, in her last car (a 99 VW Cabrio). Any advice on the better method, quickly or slowly?
PS, it’s a manual transmission
Moderation is a wonderful word. There is no need whatsoever to back out fast, unless there is a foot of snow on your driveway, and you don’t feel like shoveling. There is also the danger of maybe clipping your garage door post if your wife is a little off course. As well as colliding with another car on the street if she can’t stop fast enough once out of the driveway.
I would not worry about the whining, most reverse gears whine. She must have wrecked the VWs transmission some other way; reverse is either engaged or it is not, but shifting in gear at even half throttle is harmful.
My wife is a very spirited driver, but will not get into or out of tight places at high speed.
So what’s her top speed at the end of 25 feet of driveway? 10 mph? 15 mph? Reverse gear on any car has no trouble with that speed. Let her do it her own way. There should not be any transmission problems.
When your S.O. does this, does any part of the underside of the vehicle, i.e.: tailpipe, bumpers, skid plate(s), etc., drag on the pavement? Might be another reason to recommend that she take it a little easier pulling out onto a street/roadway. Many manual trannies whine in reverse but usually at a higher r.p.m. than what is considered to be “normal”, whatever that is. Another suggestion would be to practice, then actually doing this, backing into the garagement. She’ll certainly have a better view of any oncoming traffic from either side when leaving. Just a thought or two. (There you go again, Professor, THINKING! Your brain is gonna explode if you keep that up!).
JMHO, but I would think something in between or slow would be best.
As to reverse gear whining that is entirely normal. Reverse gears have their teeth straight cut instead of a bevel cut and this is why the whine occurs. Forward gears have a bevel cut (especially 3-5) and this is done to prevent a whining noise as you drive.
With the reverse gear knocked out of the previous VW I would think that would probably be caused by either firmly yanking the gear lever into reverse all of the time or forcing the gear lever into reverse while the car has a dragging clutch (due to worn clutch, faulty adjustment/hydraulics, etc.).
That would take an examination of the faulty gear set to determine.
Based on your description of her hammering it then it sounds to me like her method is not working too well and she’s probably also hammering that gear lever into reverse. It’s not a matter of speed so much as technique.
Guess she’ll hate me now. 
Is she open to our suggestions? If so, she should slow down and take it easier. If she’s already blown one reverse gear, she’s obviously in too much of a hurry. The reverse gear is small, a tiny gear pushing the car rearward, and it isn’t meant for drag racing up a hill.
If not, you simply cannot win this anyway, so find something to concern yourself with that you CAN affect.
I blew the side of the transmission completely off in my 49 Chevy pick-up 3-speed while backing up a hill fast,got to the top and could drive the 5 or so miles home.