The cooking time for a rump roast that weighs 2 to 4 pounds is 1 1/2 to two hours at 325 degrees Fahrenheit. To achieve medium-rare doneness, the roast should come out of the oven when a meat thermometer registers the internal temperature at 135 degrees Fahrenheit.
For medium doneness, the roast should stay in the oven until its internal temperature reaches 150 degrees Fahrenheit. A well-done roast stays in the oven until it registers 160 degrees Fahrenheit. Regardless of the level of doneness, once the roast is out of the oven, it should rest for 10 to 15 minutes or until the internal temperature increases by 10 degrees Fahrenheit.