Answer:
12 days
3 degrees
Step-by-step explanation:
Let y be the temperature of the cities after x days have passed.
Temperature of New York City
[tex]y=-3+\dfrac{1}{2}x[/tex]
In Juneau the temperature falls by 1 degree per 4 days. So, in 1 day the temperature falls be [tex]\dfrac{1}{4}[/tex] degree.
The minus sign is due to the fact that the temperature is falling
Temperature in Juneau Alaska
[tex]y=6-\dfrac{1}{4}x[/tex]
We need to find the value of x for which y will be equal
[tex]-3+\dfrac{1}{2}x=6-\dfrac{1}{4}x\\\Rightarrow \dfrac{1}{2}x+\dfrac{1}{4}x=6+3\\\Rightarrow \dfrac{3}{4}x=9\\\Rightarrow x=\\\Rightarrow x=9\times \dfrac{4}{3}\\\Rightarrow x=12\ \text{days}[/tex]
[tex]y=-3+\dfrac{1}{2}x=-3+\dfrac{1}{2}\times 12\\\Rightarrow y=3\ \text{degrees}[/tex]
Hence, in 12 days the temperature will be same in both the cities will be 3 degrees.
