The question was asked in another forum but there were a lot of just plain ignorant and stupid answers and the topic died but I think it might be a good thought experiment. The question is
Is it faster to boil 10 L of water all at once (in a 10L pot) or 10 L of water in 1 L pots successively?
This is an example of a question that cannot be answered as given, as it will depend on so many unstated assumptions. Each person answering the question may make different assumptions, and so may arrive at as different answer.
The only way to address this question is not to answer it, but to discuss the kinds of assumptions that might need to be made to give an effective answer.
We can give a "spherical cow" answer, by making some very unrealistic assumptions:
1. In both cases we have the same mass of water (10 L = 10 kg)
2. In both cases we are heating the water from the same starting temperature to the same ending temperature (e.g. from 20°C to 100°C).
3. In both cases the rate of heating is identical (e.g. 3 kW)
4. All the heat added goes into the water and none is wasted
5. No heat escapes from the water to the surroundings (perfectly insulated containers)
6. No boiling or evaporation occurs (which will consume additional heat beyond that required for raising the temperature)
By making assumptions such as these, we can observe that the time to bring the 10 kg of water to boiling point will be identical in both cases, since heating water without losses is a path-independent process. To raise a given mass of water from one temperature to another will require the same amount of energy regardless of whether you do it in pieces or as a whole. If the power input is the same in all cases, then the time taken will also be the same.
Now, by varying or relaxing the listed assumptions above, such as by allowing for heat losses, then the answers can change, and this is where the interest may lie.