Problem:
David drives from his home to the airport to catch a flight. He drives miles in the first hour, but realizes that he will be hour late if he continues at this speed. He increases his speed by miles per hour for the rest of the way to the airport and arrives minutes early. How many miles is the airport from his home?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Let be the remaining distance after one hour of driving, and let be the remaining time until his flight. Then , and . Solving gives and . The total distance from home to the airport is miles.
Let be the distance between David's home and the airport. The time required to drive the entire distance at is hours. The time required to drive at for the first miles and for the remaining miles is . The second trip is hours quicker than the first, so
Solving yields miles.
The problems on this page are the property of the MAA's American Mathematics Competitions