From your understanding of the relationship between temperature and pressure, what temperature would boiling water attain in the open pot of a backpacker camping at 10,000 feet above sea level where the air pressure is about third of the pressure at sea level? does water boil faster or slower at that elevation?

The water will boil at lower temperature and faster at higher altitude/elevation.

Explanation

Boiling point, the temperature at which the liquid starts to break their bonds and starts to vaporize.

The mechanism at that point is that the internal vapor pressure of the liquid will be equal with the surrounding pressure in order to get vaporize.

So the boiling point or boiling temperature is the external heat transferred to the liquid so that the liquid's internal vapor pressure will be equal with the surrounding pressure.

As in higher altitudes the pressure is less, so lesser energy is required to boil the liquid. While, in water, the boiling point is 100 deg Celsius at sea level.

But when the same water molecules will be heated at higher altitude of about 10000 ft above sea level, the boiling temperature will be less than 100 °C and the boiling point will be reached faster than the time taken to achieve the boiling temperature of water at sea level.

This is because, at higher altitude the surrounding pressure will be less, so the external heat energy required to equate the internal vapor pressure of water with surrounding pressure will be less.

Thus, the water boils at lower temperature and faster at the elevation.