Physics - Boiling Potatoes in Water

Question: Will potatoes cook faster if the water is boiling faster?

My lecture notes say no, apparently because water stays at the same temperature (and that determines how fast the potatoes cook). But the fact that water boils faster within a specified timeframe means that more energy is being supplied to the potatoes within a certain period of time. (imagine plotting a graph of temperature versus time, the area under the curve (energy supplied) is greater if the water boils faster).

Hope somebody can clarify this point. Thanks.

exactly you are supplying greater energy if the water is boiling faster and that energy is not transferred to the potatoes but to water to change its state from the liquid to gaseous state.
so the energy is not actually going through potatoes.

comment if you have any doubts.

EDIT: -
no. it is not to do with the water's high heat capacity but with the water's boiling point.
at a fixed pressure, a liquid cannot maintain it's bonds over a certain temperature, hence the bonds break and the water changes into gaseous state.
so it just cant go to higher temperature.

and for it to transfer heat to the potato the temperature of the potato must be less than that of water, that is the basic criteria for heat to flow.
and for more heat to flow more must be the temperature difference.
like if the a 20 K difference would cause more heat to flow than a difference of 10 K
so the heat transferred to the potato depends on the temperature of the water and as i have explained water cannot go at higher temperature.
hence rate of boiling doesn't matter

Water boils at a certain temperature, that's it. Putting it on more heat will bring it to a boil faster, but it will not make the boiling water any hotter. If you apply enough heat and/or time all the water will turn to steam and you'll have an empty pot. When water reaches a certain temperature it turns into a gas (steam), just like any matter. The actual temperature depends on the pressure, this is why some recipes give you a different cooking time if you're in the mountains. You can cause the potatoes to cook faster by putting them into a pressure cooker, which is why they exist. When water is in a pressure cooker it's under high pressure, water boils at a higher temperature when under higher pressure, so the water the potatoes are boiling in is hotter than if the water was in a normal pot.

Your notes are correct - , supplying more heat does not increase the temperature of the water, the extra energy is used to change the phase of the water from liquid to gas. i.e. the water boils more quickly.The temperature stays the same.
This is an important propery in physics. It known as latent heat.

Same applies to an ice bath - if you have ice and water in an ice bath. As the temperature of the water/ice at zero degrees increases, the heat is used by the ice at zero to change to water at zero. This helps the temperature of the mixture stay stable for a long time.