smc

Question

At noon on a certain day, Minneapolis is N degrees warmer than St. Louis. At 4:00 the temperature in Minneapolis has fallen by 5 degrees while the temperature in St. Louis has risen by 3 degrees, at which time the temperatures in the two cities differ by 2 degrees. What is the product of all possible values of N?

Accepted Answer

At noon on a certain day, let M and L be the temperatures (in degrees) in Minneapolis and St. Louis, respectively. It follows that M=L+N. At 4:00, we get align* |(M-5)-(L+3)| &= 2 |M-L-8| &= 2 |N-8| &= 2. align* We have two cases: 1. If N-8=2, then N=10. 2. If N-8=-2, then N=6. Together, the product of all possible values of N is 106=: 60.