Problem:
At noon on a certain day, Minneapolis is degrees warmer than St. Louis. At the temperature in Minneapolis has fallen by degrees while the temperature in St. Louis has risen by degrees, at which time the temperatures in the two cities differ by degrees. What is the product of all possible values of ?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
At noon on a certain day, let and be the temperatures (in degrees) in Minneapolis and St. Louis, respectively.
It follows that
At 4:00, we get
We have two cases:
. If , then .
. If , then .
Together, the product of all possible values of is .
The problems on this page are the property of the MAA's American Mathematics Competitions