Final answer:
The family must drive 15 mph over the speed limit for the first part of the trip to arrive in 4 hours. For the first 115 miles, they must drive at 70 mph, which matches the speed limit of the last 165 miles, thus no extra speed is required for the second part option A is correct.
Step-by-step explanation:
The question asks how much faster the family must drive over the speed limits to cover the total distance in 4 hours.
First, we calculate the time it would take to travel at the speed limits:
- Time for 115 miles at 55 mph: 115 miles / 55 mph = 2.09 hours
- Time for 165 miles at 70 mph: 165 miles / 70 mph = 2.36 hours
Combining the times gives us: 2.09 hours + 2.36 hours = 4.45 hours
Now, they want to finish the trip in 4 hours. Hence, we must find the extra speed needed to decrease the time from 4.45 hours to 4 hours over the total distance of 280 miles (115+165 miles):
Distance = Speed × Time
Speed = Distance / Time
Speed Needed = 280 miles / 4 hours = 70 mph
Therefore, to go 115 miles at 70 mph, they are already driving at the speed limit for the last part of the trip, but they need to drive 15 mph faster than the 55 mph limit for the first part.
The correct answer to how much faster they would need to drive over the speed limits to arrive in 4 hours for the entire trip is 15 mph only for the first part of the trip, because for the second part, no increase is needed.
Option A) 15 mph is the correct choice.