Final answer:
Alan has completed 1/4 of his journey in 4.25 hours at a speed of 64 km/h. The total distance of the journey is 1088 km. He needs to travel at an average speed of approximately 96 km/h to complete the remaining journey in 8.5 hours.
Step-by-step explanation:
Alan took 4 hours and 15 minutes to travel 1/4 of a journey at an average speed of 64 km/h. To find out the total distance for the journey, we multiply the time by the speed. First, convert 4 hours and 15 minutes to just hours, which is 4.25 hours. Thus, the distance for this first 1/4 of the journey is 4.25 hours * 64 km/h = 272 km. Hence, the total journey is four times this distance, which is 272 km * 4 = 1088 km.Next, we need to calculate what pace Alan must maintain to complete the remaining 3/4 of his journey within a certain timeframe. Alan wants to complete the entire journey in 12 hours and 45 minutes, or 12.75 hours. Since he has already spent 4.25 hours, he has 12.75 hours - 4.25 hours = 8.5 hours left to travel the remaining 816 km (which is 1088 km - 272 km already traveled).To find the required average speed to cover the remaining distance in the time left, we divide the remaining distance by the time remaining. Thus, the required average speed is 816 km / 8.5 hours which is approximately 96 km/h.