Problem:
Along the route of a bicycle race, water stations are evenly spaced between the start and finish lines, as shown in the figure below. There are also repair stations evenly spaced between the start and finish lines. The water station is located miles after the repair station. How long is the race in miles?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The rd water station is located of the way along the race (the water stations split the race up into equal spaces). The first repair station is located of the way along the race. The distance between the two is the length of the race. We know that this equals , which means the race is miles long.
Thus, is the correct answer.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions