This "group quote" is from George Mallory and Everest. The advice is as good today as it was in 1922, even on a moderate mountain like Whitney where altitude-effect is a major factor
The climbers are not of course competing to reach the goal one before another, the aim is for all to reach it. But the climbers’ performance, like the runners’, will depend on two factors, endurance and pace
George Mallory, Chapters IV-VI, X-XI in
Bruce, CG. The Assault on Mount Everest 1922 p 125-6
Your pace at altitude will be slower. Just think, above the 10,000 ft mark, air pressure (and therefore oxygen availablity) will fall below 2/3 of normal.