Search and Rescue, Mountain, modern day

Modern day, Colorado.

I have a character who is hurt while hiking a 13,000 foot peak in Colorado, while she is above treeline. It is summertime. She has not suffered serious injuries, but has hurt her ankle (and possibly her knee), so she is unable to walk well. There is a thunderstorm approaching, and other hikers who are helping her are anxious to get below treeline. In my scenario, one of them runs ahead to get help while the other two assist her down the mountain.

How would search and rescue respond to a call like this--by foot or by helicopter, or both? They are on a well-worn trail, so there would be no real "search"--it's more purely rescue.  What sort of equipment would they use to get her down off the mountain--would they carry her down in a litter? What kind of assessment would they do to determine her injuries? The trailhead is at around 10,000 feet and is at the end of a road that is difficult to access without four wheel drive. Does that make a difference in the sort of rescue performed? How and where would transfer to EMS likely be performed?

Thanks for any help!

Did a quick internet search for "search and rescue Colorado" or "mountain search and rescue". Found mostly sites for different organizations and some technical information on how to perform wilderness searches, but nothing specific for this type of scenario.