Problem:
The distance between the and exits on an interstate highway is miles. If any two exits are at least miles apart, then what is the largest number of miles there can be between two consecutive exits that are between the and exits?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
There are segments between the and exits. Using the minimum length of miles, segments would yield miles. This leaves miles for the other segment.
There are segments between the and exits. If each segment were its minimal miles length, then the total distance between the and exits would be miles. Since , all additional miles could occur between one pair of consecutive exits. Such a pair would be miles apart.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions