Final answer:
Joe is not in violation of Illinois vehicle law regarding the transportation or possession of alcoholic liquor in a motor vehicle as long as his blood-alcohol concentration is not over the legal limit.
Step-by-step explanation:
According to the information provided, Joe is not in violation of Illinois vehicle law regarding the transportation or possession of alcoholic liquor in a motor vehicle as long as his blood-alcohol concentration is not over the legal limit. The question states that Joe does not drink the beer while he is driving, which means he is not consuming alcohol while operating a vehicle. However, it is important to note that laws regarding the transportation of alcohol may vary by state, so it's always advisable to familiarize oneself with the specific laws and regulations in one's jurisdiction.