Final answer:
To complete the 460-mile trip in 10 hours after driving at 50 mph for the first 6 hours, the motorist must average 40 miles per hour for the remaining 4 hours.
Step-by-step explanation:
The question asks how fast a motorist must drive in the remaining 4 hours to complete a 460-mile trip in 10 hours if she has already been driving at 50 miles per hour for the first 6 hours. To solve this, let's calculate the distance covered in the first 6 hours:
Distance covered in 6 hours = 6 hours × 50 miles per hour = 300 miles
Remaining distance to cover = Total distance - Distance already covered = 460 miles - 300 miles = 160 miles
The motorist has 4 hours left to cover the remaining 160 miles. To find the required average speed for the remaining distance, we use the formula:
Average speed = Distance / Time
Required average speed for the remaining 4 hours = 160 miles / 4 hours = 40 miles per hour
Therefore, the motorist must average 40 miles per hour for the remaining 4 hours to reach her goal.