The higher the pressure, the higher boiling point of water. At lower the pressure, the boiling point of water comes down. So, the lower pressure inreases the boiling resulting more evaporation. As we go higher in altitude, the atmospheric pressure decreases. This results in decreasing the boiling point at higher altitude and increase in boiling of water. In fact, at the sea level ,the the sea water boils at 100 degree C where atmospheric pressre is normal. However , the boiling takes place at a lower temperature at the top of a mountain due to low pressure. In other words the boling is faster at the top of a mountain than that at its foot.
For example, at the altitude of 8850m, on Everest,water boils at 69 Celsius degrees, compared to sea level, where water is boiling at 100 Celsius degrees.The explanation comes from the fact that on the top of the mountain the air pressure is the third part of the one at sea level. There is a rule which states that with each extra Km of altitude, the water is boiling at a temperature which is 3.33 Celsius degrees less than the initial one (at the "0" level or "sea level").
The boiling point water among other thing, is dependent on the atmospheric pressure where the water is being heated in open, Lower the atmospheric pressure lower the boiling point of water.
As the atmospheric pressure decreases with altitude, it will be lower at the top of mountain as compared to the foot of mountain. Because of this the water will start boiling at lower temperature at the top of mountain as compared to bottom of mountain.
Because of this, with the same amount of heat applied to a given mass of water, the water will reach its boiling point earlier and therefore boil faster at top of mountain as compared to at bottom of mountain.