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.
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