Answer:
It will be 4 hours until the temperatures are the same
Step-by-step explanation:
Let [tex]T_{c}[/tex] represent the temperature in Coldspot in [tex]x[/tex] hours and
[tex]T_{f}[/tex] represent the temperature in Frostberg in [tex]x[/tex] hours.
From the question,
The temperature in Coldspot is -7° and is increasing 2.5° per hour, then we can write that
[tex]T_{c} = -7 + 2.5x[/tex]
Also, from the question,
The temperature in Frostberg is 19° and is decreasing 4° per hour, then we can write that
[tex]T_{f} = 19 - 4x[/tex]
To determine how long it will be until the temperatures are the same, that is when [tex]T_{c}[/tex] will be equal to [tex]T_{f}[/tex], we will equate the two equations and determine [tex]x[/tex].
[tex]x[/tex] will give the number of hours until the temperatures are the same.
[tex]T_{c} = T_{f}[/tex]
[tex]-7 + 2.5x = 19 - 4x[/tex]
Then,
[tex]4x + 2.5x = 19 + 7[/tex]
[tex]6.5x = 26[/tex]
[tex]x = \frac{26}{6.5}[/tex]
∴ [tex]x = 4[/tex]
Hence, it will be 4 hours until the temperatures are the same.
