Question

At noon on a certain day, Minneapolis is N degrees warmer than St. Louis. At 4:00 the temperature in Minneapolis has fallenby 5 degrees while the temperature in St. Louis has risen by 3 degrees, at which time the temperatures in the two cities differby 2 degrees. What is the product of all possible values of N?A 10 B 30C 60D 100E 120

Answer 1

We are given the information about two different cities. So, what we will try to do is find a function that describes the temperature in each city.

Consider x =0 to be noon and consider x to be "x hours after noon". Let M(x) be the function that describes the temperature at Minneapolis and S(x) the function that describes the temperature at St. Louis.

We are told that at noon, Minneapolis is N degrees warmer than St. Louis. This means that if we take the temperature of St. Louis at Noon and add N to it, we get the temperature at Minneapolis at noon. Using our notation, we get the following equation

$M(0)=S(0)+N$

At 4, we have x=4. We are told that after 4 hours the temperature in Minneapolis has decreased by 5 degrees and that the temperature in St. Louis has increased by 3 degrees. This translates to the following equations

$M(4)=M(0)\text{ -5 = S(0)+N -5}$$S(4)=S(0)+3$

Let us assume that the temperature increase or decrease in a linear fashion. That is, we are going to find a linear function that models both temperatures.

Recall that the line equation in the slope intercept form, we will

So for M(x) we are given the points (0,S(0)+N) and (4,S(0)+N -5)