On a winter evening at sundown, a Kansas City news station reports that the temperature is $-2 \, ^{\circ}\mathrm{F}$ and will drop by $2 \, ^{\circ}\mathrm{F}$ per hour until sunrise. At the same time, a Chicago news station reports that the temperature is $6 \, ^{\circ}\mathrm{F}$ and will drop by $4 \, ^{\circ}\mathrm{F}$ per hour. $\newline$ Which equation can you use to find $h$ , the number of hours it will take the cities to reach the same temperature? $\newline$ Choices: $\newline$ (A) $2h - 2 = 6h - 4$ $\newline$ (B) $-2 - 2h = 6 - 4h$ $\newline$ How long will it take for the cities to reach the same temperature? $\newline$ Simplify any fractions. $\newline$ $\_\_\_\_$ hours $\newline$

Full solution

Q. On a winter evening at sundown, a Kansas City news station reports that the temperature is

-2 \, ^{\circ}\mathrm{F}

and will drop by

2 \, ^{\circ}\mathrm{F}

per hour until sunrise. At the same time, a Chicago news station reports that the temperature is

6 \, ^{\circ}\mathrm{F}

and will drop by

4 \, ^{\circ}\mathrm{F}

per hour.

\newline

Which equation can you use to find

h

, the number of hours it will take the cities to reach the same temperature?

\newline

Choices:

\newline

(A)

2h - 2 = 6h - 4

\newline

(B)

-2 - 2h = 6 - 4h

\newline

How long will it take for the cities to reach the same temperature?

\newline

Simplify any fractions.

\newline

\_\_\_\_

hours

\newline

Identify Equation: Identify the correct equation to represent the situation. Kansas City's temperature starts at $-2 \degree\text{F}$ and drops by $2 \degree\text{F}$ per hour, so its temperature after $h$ hours is $-2 - 2h$ . Chicago's temperature starts at $6 \degree\text{F}$ and drops by $4 \degree\text{F}$ per hour, so its temperature after $h$ hours is $6 - 4h$ . Set these equal to find when the temperatures are the same: $-2 - 2h = 6 - 4h$ .
Add $4$ h: Solve the equation $-2 - 2h = 6 - 4h$ . First, add $4h$ to both sides to get $-2 + 2h = 6$ .
Add $2$ : Next, add $2$ to both sides to isolate the term with $h$ : $2h = 8$ .
Divide by $2$ : Finally, divide both sides by $2$ to solve for $h$ : $h = \frac{8}{2} = 4$ .