This question comes from a chemistry test that i got back.
I'm posting this on physics.stackexchange because i feel that i don't get the physics side of it. 

We learned that temperature increases the speed at which a reaction occurs. (This I do get: the more temperature/speed of molecules/kinetic energy, the harder and more frequently the atoms interact with each other $\to$ more products are formed) However I only get it when the pressure is held constant.

Now the question:

> 
> High in the mountains, water cooks at 97°C (instead of 100). How will that influence the time it takes to cook food with the steam (eg by placing the food in a pan above a pot of boiling water) ?
> 
> 
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The answer: It will take longer. My answer: It will take the same amount (excluding warming the pot of water).

What I don't get is this: 

I see why the water cooks at 3°C lower in the mountains versus on the ground, that is because there is less atmospheric pressure pushing down on the water. 

But in both cases I'd think that when the water 'cooks', the water molecules break apart from eachother with the same kinetic energy. That is, water cooks when the pressure of the air around it is equal to the pressure of the water, with the pressure proportional to the temperature. 
Now if the pressure of the air is less than on the ground we also have to add less pressure to the water to get AN EQUAL EFFECT (the water molecules breaking apart from each other / cooking) so I don't get how the kinetic energy of the steam would be different. The "extra" kinetic energy of the water on the ground would have gone into overcoming the air pressure.

I think of it like counteracting forces, sure the force on the water by the air is less in the mountains than when on the ground but the temperature is also 3°C less. Where has my reasoning gone wrong? 

[![enter image description here](https://i.stack.imgur.com/XkcAz.png)](https://i.stack.imgur.com/XkcAz.png)

Wouldn't the kinetic energy of the steam in the two situations be the same?

I know this is a lengthy question with a lot of text but I don't know how to express it otherwise.