Final answer:
Joe covered a total distance of 150 miles by running for 20 minutes at a rate of 3 mph and 15 minutes at a rate of 6 mph.
Step-by-step explanation:
To find the total distance covered by Joe, we can calculate the distance covered in each segment and sum them up. In the first segment, Joe ran for 20 minutes at a rate of 3 mph, so the distance covered is 20 minutes * 3 mph = 60 miles. In the second segment, Joe ran for 15 minutes at a rate of 6 mph, so the distance covered is 15 minutes * 6 mph = 90 miles. Adding up the distances, the total distance covered by Joe is 60 miles + 90 miles = 150 miles. Therefore, none of the given options (1) 30 miles, (2) 45 miles, (3) 60 miles, or (4) 75 miles are correct.