I have a roast that needs 1 1/2 hrs at 315 and a chicken that needs 2 hrs at 350. How do I cook them both in one oven?

Using one temperature is fine, but you are increasing the mass of product in the oven so it will take a bit longer. Use a thermometer - especially on the roast ... no problem in pulling it out to rest while the chicken finishes.
Rotate the two in the oven to avoid hot and cold spots which can result in having one side done and the other not.

Chicken doesn't mind being done at 315, it just needs longer in the oven. Give it about 40 to 45 min at 350, then turn down the oven for the roast and cook for the 1 1/2 hours needed. The chicken may not have as crispy a skin but it will be more tender and juicy.

What is the roast that is cooking at 315? A roast should be perfectly fine at 350 -- so long as you're using a thermometer to gauge doneness -- so I would say to use the same 350 oven for both! (Just start the chicken earlier, of course.)