Why does it takes longer to hard boil and egg at high altitudes than at sea level?

In high altitudes the atmospheric pressure is lower than at sea level. Then, this means that the boiling point of water on the higher altitude is lower.

All cooking processes are directly affected by atmospheric pressure.

At sea level, water boils at 212º F, but on mountaintops and other high-altitude regions, the boiling point is much lower.

For about every 500 feet of ascent, the boiling point is lowered 1ºF.

At a 7,000 foot elevation, water would boil at about 198º F. Because the water is boiling at a lower temperature, it would take longer to cook food by boiling.
Hard Boiled Eggs High Altitude
Because, as we go to higher altitudes, the boiling temperature of water decreases. It therefore takes longer, not to boil the water (that will be quicker at the lower temp.), but for the heat of the lower temperature to get through the item being boiled.

(It’s difficult to get a decent cup of tea too…takes longer to infuse (if it brews at all).
Because atmospheric pressure decreases at high altitudes and pressure is what increases the speed of heating.
the boiling point decreases