Originally Posted by Metaluna

On extreme hill climbs, there's not a lot of difference between being on foot and on a bike. For example, there are annual bike and foot races up Mt. Washington in New Hampshire, and if you compare the winning times of both, they are in the same ballpark (typically about 55-65 minutes for a 7.6 mile climb at 12% average grade). Compare that, to say, a conventional marathon where even a casual cyclist can easily beat the time of a world class runner (about 2 hrs).

So the upshot is that the runner in your case wasn't particularly handicapped by being on foot, like she would have been on level ground. So personally, I wouldn't be any more freaked out by this than I would be if I were passed by another cyclist. It just means you encountered someone in slightly better shape, or more well-rested, or just starting out on their run etc.