Final answer:
The food delivery driver will drive 432.5 miles east to reach the restaurant, which includes arriving at the library and then covering the additional distance to the restaurant east of it.
Step-by-step explanation:
When a food delivery driver is 434 miles west of a city's library and needs to reach a restaurant that is 1.5 miles east of the library, the driver would have to drive to the library first and then continue east for another 1.5 miles. To calculate the total distance, you subtract the 1.5 miles from the 434 miles to find how far the driver will drive east.
Therefore, the correct distance the driver will drive east is:
434 miles - 1.5 miles = 432.5 miles east.
The driver will drive 432.5 miles east to the library and then additional 1.5 miles to arrive at the restaurant, thus the most direct route for him would be option 1.