Does rate of heating of water change with altitude? I was recently on a trip at 5,000 feet with a bunch of people I don't know well, all of whom swore that water "takes longer to boil" at higher altitudes. I'm pretty sure they were confusing boiling time with cooking time (which is longer for boiled foods at altitude because the boiling point of water is lower there). 
My offered suggestions (stronger stoves at home, weaker stoves in vacation rentals; more leisure to watch the pot leading to perception of longer boiling) were rejected out of hand. 
Boiling time should be shorter at altitude because the boiling point is lower, right? But is there any sense in which my travel buddies might be right? Is there any effect of altitude on the rate of heating of the water?
 A: You are right in your explanation. It doesn't take longer to boil water. Rather it takes longer to cook food using water because less heat is transferred to the ingeredients by radiation or conduction. About the "rate of heating" of water, the higher you go the shorter it takes to heat water. Hence, the rate of reaching the temperature of boiling increases. How do you define "rate of heating"? Do you mean rate of energy transfer to the ingredients?
A: You are right that it is misconception.
Does rate of heating of water change with altitude?
No.
Boiling time should be shorter at altitude because the boiling point is lower, right?
The lower air pressure allows the water to evaporate easier and will boil off faster, therefore it will take longer for the water to reach a rolling boil. You can see a similar effect by boiling water with a lid on the pan compared to without a lid.
But is there any sense in which my travel buddies might be right?
I believe they are thinking of a rolling boil and then inferring that the whole process is taking longer.
Air crew on flights boil water for cups of tea etc. The cabin is pressurised to prevent altitude sickness, but also allows them to boil the water like you would on the ground.
