Thanks, but I wish it was a selfless one. I have always been scared of pulling off a rock and killing my belayer, so, as a human with rational self interest, this is the most effective way to live if you kill your belayer while sport climbing.
You've got a second rope hanging next to you? Then you can get up pretty effectively with no equipment.
Tie an overhand loop in the free rope around thigh level. Put both feet in it and stand up, screaming "take!" at the belayer who yards in the rope with as much tension as possible. Take your feet out of the loop (you are now hanging at or near the higher level achieved by standing up in the overhand loop), untie it (or not if you are really pumped) and tie a new overhand loop at your new higher thigh level. Repeat until you can continue climbing or until you reach the top.
If your feet can take the pressure, you can forget the overhand loop and just wrap the hanging line around your feet four or five times and stand up on that. (You bring your knees to your chest and do the wrapping in that position so you get a good stand-up.) It will probably get painful if you have to repeat this many times, but if you only have to gain a ten feet or so to get out of trouble, this will work.
Try to get your feet as high as possible while still being able to stand up, because you will lose some ground to rope stretch. (If the hanging line is a static rope, so much the better.)
If there is a second person up there who can belay, then they can go on belay on the second rope and haul the original foot loop up every time you unweight it by hanging on the original belay line. This method goes pretty quickly.
All that said, ascending a rope with prussiks (or other friction knots) is a basic skill that all climbers need to be able to do.
Kyle, since you have two ropes and I assume the climbing is not overhanging, I would simply keep them on a direct belay and get them to batman up the fixed line with their feet on the rock as you belay them up. If their hands are soft, aid gloves will help.
This means that they can get over the hard bits but still enjoy the rest of the climb and don't need to know how to do anything or faff around clipping stuff on and off the rope.