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I'm not a scientist, but let me try and answer this.
I think the question is ambivalent. The water would boil "faster" on the mountain if the starting temperature of water at sea level and at an altitude of 1 km was the same; just like in a race all runners start at the same starting point.
You would expect water to boil faster on the mountain due to the lower atmospheric pressure, which in turn lowers the boiling point.
I am assuming that if the boiling point of water decreases as the atmospheric pressure decreases then the freezing point would proportionally decrease too (from the rule: 0 degrees celsius to -3.33 for every km). Is that assumption correct?
If that assumption is correct then the following question is: "What is the starting temperature of the water on the mountain as opposed to at sea level?" So the answer depends on the starting temperature of the water. If the boiling point of water at an altitude of 1 km above sea level is 3.3 Degrees Celsius lower than at sea level then the time it takes for water to boil is relative to the starting temperature of the water.
Just because the boiling point is lower in the mountain does not mean that arriving at the boiling point will be faster. It could indeed be slower if the starting temperature of the water is at -30 Degrees Celsius before the heat source is applied to it.
Please correct me if my reasoning is incorrect. Thanks.
So to rephrase the question...would it be clearer to ask, "Is the boiling point of water on a mountain lower than at sea level? Secondly, assuming that the starting temperature of water, before heating it, is the same at both sea level and in the mountain where would the water boil first?"
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