Final answer:
After being stuck in traffic, the student would need to travel the remaining 16.3 miles to the airport in 22 minutes. To make the flight on time, the student must maintain an average speed of approximately 44.44 miles per hour for the rest of the trip.
Step-by-step explanation:
To figure out the average speed you must have for the remaining distance to the airport after being caught in traffic, we first need to calculate the distance already traveled and the time remaining. We're given that the student drives for 18 minutes at an average speed of 19 miles per hour. Now, convert minutes to hours by dividing by 60, so the time spent is 18 minutes / 60 = 0.3 hours. The distance traveled in that time is 19 mi/hr × 0.3 hours = 5.7 miles.
The total distance to the airport is 22 miles. Deducting the portion already traveled, we get 22 miles - 5.7 miles = 16.3 miles left to cover. The total time allotted for the trip is 40 minutes, and having already spent 18 minutes, there is 40 minutes - 18 minutes = 22 minutes, or 22 minutes / 60 = 0.3667 hours left to make to the airport.
To find out the required average speed for the remaining distance, we use the formula speed = distance / time. Hence, the needed speed is 16.3 miles / 0.3667 hours = 44.44 mi/hr (rounded to two decimal places). Therefore, the average speed the student must maintain for the rest of the trip to reach the airport in time is approximately 44.44 miles per hour.