General knowledge would tell us that a higher altitude means a lower pressure. That would explain why airplanes have to be pressurized. By this alone, we can already assume that cooking at sea level would be faster than cooking on a mountain top. More pressure increases rate of reaction afterall.
At the same time, there is also vapor pressure experienced by an egg cooked just a bit above sea level than one cooked in a mountain. The vapor that arises from the ocean has its own pressure so this would add on to the rate of cooking the egg.
Additionally, temperature plays a very big role in cooking or rates of reaction. We all know that temperature in mountain tops would be much less than that just a bit above sea level. Of course since there is more pressure “below,” there is more temperature “below” as well.
[Could not think of how to do a story line …]