A general guideline for cooking a rib roast is between 13 and 20 minutes per pound. Cooking time also greatly depends on whether the roast is to be slow-cooked on low heat or simply cooked through on high heat.
According to Allrecipes.com, rib eye roasts can either be cooked for a longer time at a lower temperature or for a shorter time at a higher temperature. Cook a roast for 17 to 20 minutes per pound if cooking at 325 degrees Fahrenheit and 13 to 15 minutes per pound if cooking at 450 degrees Fahrenheit. These cooking times yield different results, as roasts cooked low and slow are larger and juicier, while roasts cooked at higher temperatures have a better-seared exterior. The two methods can be combined by first searing the outside at a higher temperature and then lowering the temperature for the last 30 to 45 minutes of cook time.