Maybe everyone already knows this, so please excuse if so. At higher elevation and lower pressure, water boils at a lower temperature, so you should not have to use as much fuel to bring it to a boil (unless the flame burns cooler for some reason). However, the water will stay at its boiling point temperature until it's completely boiled away, so that's why food takes longer to cook at altitude. You are cooking it at a lower temperature.

My chemistry professor used to do a demonstration with a small vacuum chamber and a cup of water. He would lower the pressure inside the chamber until the water would boil, at room temperature.