Final answer:
To achieve an overall average speed of 56 mph, you must maintain an average speed of approximately 84 mph for the remaining 49 miles.
Step-by-step explanation:
To determine the average speed you must maintain for the remaining distance to achieve an overall average speed of 56 mph, we need to consider the total time taken for the entire trip. The total distance for the trip is 98 miles. Halfway through the trip (49 miles), you have averaged only 42 mph.
Firstly, to find the time taken to travel the first 49 miles at 42 mph, you can use the formula time = distance ÷ speed. That gives us time = 49 miles ÷ 42 mph = 1.1667 hours.
To have an average speed of 56 mph for the entire 98 miles, the total time taken should be total time = total distance ÷ average speed = 98 miles ÷ 56 mph = 1.75 hours.
The remaining time to complete the trip to maintain the average of 56 mph would be 1.75 hours - 1.1667 hours = 0.5833 hours.
The average speed required for the remaining 49 miles can be found using the formula speed = distance ÷ time. Thus, speed = 49 miles ÷ 0.5833 hours ≈ 84 mph.
You need to maintain an average speed of approximately 84 mph for the remaining distance to achieve an overall average speed of 56 mph.