Final answer:
Andrew needs to drive back at an average speed of approximately 58.65 miles per hour to cover the distance of 78 miles in 80 minutes and reach home on time.
Step-by-step explanation:
The student's question involves calculating the speed needed to return home in a shorter amount of time than the trip took initially. Andrew drove from Aurora to Zalesville in 1.5 hours (which is 90 minutes) at an average speed of 52 miles per hour. To find out how fast he must drive back to reach home in 80 minutes, we first calculate the distance traveled using the formula: Distance = Speed × Time .
So, the distance from Aurora to Zalesville is 52 miles/hour × 1.5 hours = 78 miles. Now, using the formula Speed = Distance / Time, we need to find out the speed required to travel 78 miles in 80 minutes (1.33 hours). The required speed is 78 miles / 1.33 hours = 58.65 miles/hour (rounded to two decimal places). Thus, Andrew needs to drive back at an average speed of approximately 58.65 miles per hour to reach home in 80 minutes.