Baking – How to adjust oven temperature/time to have two dishes ready at the same time

talon8 is absolutely right: the best way to go about this is to use a thermometer. However, it is still an interesting question how the expected cooking time varies with the weight of a roast.

It is such an interesting question that in 1961, SIAM Review published a scholarly article entitled "On Cooking a Roast". To be a bit more precise, the question that the authors answer is this: Suppose we have two roasts with exactly the same combination of identical tissues, and the same shape except that the one is a scaled (blown up) version of the other. Let's weigh both roasts and compute the ratio between the two weights; let's call that ratio r. Suppose furthermore that the roasts have the same starting temperature, and we will cook both until they have both reached some given (higher) temperature at their centre. What can we say about the times that both roasts need to cook for?

The answer is that under these assumptions, the bigger roast will need r^(2/3) times as long as the smaller one.

So, assuming each small roast (700 and 950 grams) has the same shape as the big one that the recipe writers used (let's say 1750 grams), for the 950 gram roast you'd expect to use (950 / 1750)^(2/3) = 0.665 or about two-thirds of the cooking time, and for the 700 gram one you'd expect to use (700 / 1750)^(2/3) = 0.543 or just over half of the cooking time. In particular, for the 950 gram roast, you should expect to roast it at 200C for 20 minutes, then turn down to 180 and roast for around 0.665 * 1750 / 450 * 12.5 = 32 minutes more. (1750 / 450 * 12.5 = 49 minutes is the average time they would recommend for the 1750 gram roast, and we're using that as the base for comparing our 950 gram roast against.) Then check with your thermometer!

Finally, I think for the resting time, you might as well use the original 30 minutes, because that's not (only) about getting the internal temperature to a certain level (although it does contribute to that - the heat will spread out through the meat), but also about things like the muscle fibers relaxing and the like, which are not covered by the article.

The ham should rest for at least 15 minutes after cooking, and probably longer than that. So you could put the potatoes into the oven when the ham has 20 or 25 minutes remaining, and then when you take the ham out, increase the temperature to 350-375F and continue cooking the potatoes while the ham rests for 15-20 minutes.