What temperature is ‘High’ in a 950 watt microwave

It may already be an implicit assumption, but I think that time to cook is probably not as important as how to cook. While the power setting does affect the time to cook, the importance of time is to control how hot the parts of the food get.

As with all cooking, there is a need to control temperature. Running the microwave at less than full power allows time for the heat to be conducted from the hot parts to the cool parts. It is similar to searing vs. sauteeing.

I think that the accuracy of most microwave oven's power settings are good enough (my own testing shows about 10%). I would be more concerned about how I wanted the item cooked. Some examples:

• When I want to reheat things like a thick soup, I run the microwave at full power for a short period of time, stir, and run the microwave again. Stirring the concoction distributes the heat faster than the conduction process.
• When I want to defrost frozen foods (think meat), I use the lowest power setting. This prevents the edges of the food from getting cooked.

1100 Watt means 1100 Joules per second (energy over time). 1100 Watt over a period of 240 seconds therefore is 264000 Joules. To deliver 264000 Joules of energy with only 800 Watt takes 330 seconds (5.5 minutes), as you expected.

As KatieK noticed, there are some additional concerns. A good recipe will tell you to let the cooked product stand for a while. This allows heat diffusion, so all those Joules of heat will be distributed well. But if you cook at lower power, then the heat will already be diffused more. I.e. at lower power, you don't need to rest the product as long.

Another difference might be that you're not just heating the product, but you're relying on a secondary effect such as killing germs. For that, you'll need to have the entire product above a critical temperature for a certain time. This in general means that you don't need to adjust the times as much as you'd expect by the simple formula.

On the other hand, a warm product will lose heat to the environment over time. I.e. not all of those 264000 Joules will stay in the product you're heating. And with more time spent at medium temperatures, there's more heat loss in a low-powered microwave.