Final answer:
It will take 4 hours for the temperatures in Coldspot and Frostberg to equalize, given that Coldspot's temperature is rising at 2.5° F per hour and Frostberg's is dropping at 4° F per hour.
Step-by-step explanation:
The student is asking how long it will take for the temperatures in Coldspot and Frostberg to be the same given that the temperature in Coldspot is -7° F and is increasing at 2.5° F per hour, while the temperature in Frostberg is 19° F and is decreasing at 4° F per hour. To solve this, we can set up an equation where the temperature change in Coldspot equals the temperature change in Frostberg. The initial temperature difference is 26° F (19 - (-7)).
Let t be the time in hours needed for the temperatures to equalize. We'll have the equation -7 + 2.5t = 19 - 4t. Combining like terms gives us 2.5t + 4t = 19 + 7, which simplifies to 6.5t = 26. Solving this, we find t = 26 / 6.5, which equals 4 hours.
Therefore, it will take 4 hours for the temperatures in Coldspot and Frostberg to be the same.