I just realized something that had never occurred to me before. I've also misplaced my tongue, though I think it might be hiding in my cheek . . .
You see, in Star Trek V, we see McCoy watching Kirk climb El Capitan. Take a look at the last pic on TrekCore's screencaps page to see how far away McCoy is:
Caps by TrekCore.com
His distance is also confirmed by the angle at which he holds the little Starfleet binoculars . . . pretty close to level instead of close to straight up. And the image through the binoculars is also confirmation . . . Kirk's area being climbed is viewed from closer to level than as if from below. Both of these can be seen in TrekCore's Chapter Two of screenshots from the film.
A few minutes later, Spock's doing his little jetboot happy dance, distracting Kirk and causing a fall. The fall takes mere seconds . . . McCoy starts running from his position toward the mountain as soon as the fall begins.
Spock and his amazing technicolor jetboots manage to save Kirk, and moments after the fall is stopped mere feet from the ground McCoy comes running up at a jog.
Surely, though, he must've gone faster than a standard human jog to make that kind of distance. He had to have run a mile or two at least, and had to have done so in well under a minute, give or take. This implies running speeds of no less than 100km/h (60mph), and probably two or three times that at least.
No wonder Dax still fondly remembered his hands. If he could move his legs that fast, just imagine what he could do with his fingers. ;)