Final answer:
To find the additional hours needed for the average speed of the entire trip to decrease to 54 mph, calculate the total distance traveled and the total time taken. Plugging in the values, we find that the additional hours needed is approximately 0.52 hours, or about 31 minutes.
Step-by-step explanation:
To find the additional hours needed for the average speed of the entire trip to decrease to 54 mph, we need to calculate the total distance traveled and the total time taken.
First, calculate the distance traveled in the first three hours: Distance = Speed x Time = 60 mph x 3 hours = 180 miles.
Next, calculate the distance traveled in the next four hours: Distance = Speed x Time = 55 mph x 4 hours = 220 miles.
To find the total distance, add the distances traveled in the first three hours and the next four hours: Total Distance = 180 miles + 220 miles = 400 miles.
Now, let's calculate the total time taken. The driver traveled at 60 mph for three hours and at 55 mph for four hours, so the total time taken is 7 hours.
To find the additional hours needed for the average speed to decrease to 54 mph, we can use the average speed formula: Average Speed = Total Distance / Total Time.
Plugging in the values, we have: 54 mph = 400 miles / (7 hours + Additional hours). Solving for Additional hours, we get: Additional hours = (400 miles / 54 mph) - 7 hours. This can be simplified to: Additional hours = (200 / 27) - 7.
Using a calculator, we find that the additional hours needed for the average speed of the entire trip to decrease to 54 mph is approximately 0.52 hours, or about 31 minutes.