I want to cook two dishes simultaneously (for efficiency's sake): carrots, which have a nominal cooking temp of 350 F / 180 C for 30 mins. and chicken, which has a nominal cooking temp of 400 F / 200 C for 45 mins. The Seasoned Advice posts I've read on this subject (here, here, here, and here) suggest the thing to do is cook at the lower temp first, then turn the oven to the higher temp; I can do that if necessary, but if possible I'd prefer to have everything in the oven at once, since the second dish cooks for a while.
If I put the carrots in at 400, how much should I reduce the cooking time? And how severely will it affect the result?