Best length for an alpine rope

Hey, after quite a stretch of focusing on purely rock climbing I'm beginning to get into snow and aline climbing. I was just wondering what lengths you all tend to prefer when it comes to choosing your alpien rope. I currently have a 70m 9.5mm rope that I use for most rock and a beater 10.2 that started out as a 60m but has since been cut to 55m due to a core shot near one of the ends. I was planning on perhaps cutting this rope down somewhere between 40m - 50m to be used as my designated alpine rope. I don't plan on doing any extremely long technical stuff, mainly just a solid rope for glacier travel, rappels and quick belays occassionally. What do you think?

The usual glacier rope length is 100 ft. or so. Most people use a half rope in the 7.7-8.5 range, to keep things light. A fat 10.2 rope can be used, but it would be a bit much to haul around with you. If you're not going to be doing more alpine routes then just go with the one of the 2 ropes that you have. 

I'd agree with most of what's been said already but may I add that it may be worth having more than one rope for alpine climbing. A glacier rope, for instance, can be a thin (8mm) 30-50m rope depending on the terrain and the number of people on the rope. This will vary. A rope you'd be using on glacier, snow AND rock would ideally be something a bit different- something in the 9mm range and anywhere from 40-60m. If you have the luxury of having any and all iterations, great. If not then my ideal ropes would be a 8mm 40m rope for glacier travel and a 9mm 60m for alpine rock, ice and some glacier travel. 

If you want a rope that you can do most everything with I prefer a 70m in the 8mm range or lighter- that is plenty long for pitching something out but you can double it up (making 35m) for glacier travel, simul-climbing, rappels, etc.   I have a 37m 7.8mm for glacier travel but it sees little use next to the other ropes I have, I only take it out when I'm not really sure whether I want a rope with me or not for alpine climbing or backcountry skiing.  Even with the extra weight I prefer the 70m if I'm taking gear, axes, crampons, etc. just because of the versatility.  

I have different ropes for different objectives. In general I'll go as light as possible. If I were going for one rope only I'd get a 60 meter half rope on the larger end of 8.5 to 8.9mm. The reason I say a half rope over a super skinny "single" ropes sacrifice sheath thickness to go with a thicker core. I've never seen an alpine rope with a soft core, I've trashed sheaths on quite a few. 

My ropes:
30M 8mm edelweiss, glacier travel for skiing volcanoes
60m 8mm mammut, routes we will be mostly simul climbing, have used as a single on pitches w/o sharp edges, party of 3, tagline for double rope raps
60m 9mm sterling nano, moderate to harder rock routes, lots of my longer multi pitch cragging, combined with the mammut for a half rope set up on wandery routes
70m 9.1mm beal joker, as above, but for longer pitches/raps (we have a lot at index that requires a 70 for the raps)

60m 8.0-8.5mm, dry treated with a middle mark.  

If you're going to be on remote glaciers in a team of two, I would recommend a 60m rope around 8 to 8.5mm, dry treated.  

Tie in for glacier travel with about 15m between climbers, and each climber carries half of the remaining length.  This gives one the ability to reach the other climber with a free end of rope in case of a serious crevasse fall, and gives you more rope to build a haul system if needed.

For rappels, you get 30m per rap without a knot to increase the chances of a stuck rope.  

For occasional technical pitches, you can do 60m if well below your limit, or double it up and use it as a double for short, harder pitches, or double it up and use as a twin for simul-climbing.