Question

Today the temperature in New York City is -3 degrees and is expected to rise one half of a degree each day. It's 6 degrees in Juneau, Alaska and expected to fall 1 degree every 4 days. How long will it take for the temperature to be the same in the two cities? What will the temperature be?

Answer 1

12 days

3 degrees

Explanation:

Let y be the temperature of the cities after x days have passed.

Temperature of New York City

`y=-3+(1)/(2)x`

In Juneau the temperature falls by 1 degree per 4 days. So, in 1 day the temperature falls be
`(1)/(4)` degree.

The minus sign is due to the fact that the temperature is falling

Temperature in Juneau Alaska

`y=6-(1)/(4)x`

We need to find the value of x for which y will be equal

`-3+(1)/(2)x=6-(1)/(4)x\\\Rightarrow (1)/(2)x+(1)/(4)x=6+3\\\Rightarrow (3)/(4)x=9\\\Rightarrow x=\\\Rightarrow x=9* (4)/(3)\\\Rightarrow x=12\ \text{days}`

`y=-3+(1)/(2)x=-3+(1)/(2)* 12\\\Rightarrow y=3\ \text{degrees}`

Hence, in 12 days the temperature will be same in both the cities will be 3 degrees.