One morning in Austin, Texas, the temperature was $80 \, ^{\circ}\mathrm{F}$ and rose by $2 \, ^{\circ}\mathrm{F}$ per hour until midafternoon. At the same time in Little Rock, Arkansas, the temperature was $72 \, ^{\circ}\mathrm{F}$ and rose by $4 \, ^{\circ}\mathrm{F}$ per hour. $\newline$ Which equation can you use to find $h$ , the number of hours it took for the cities to reach the same temperature? $\newline$ Choices: $\newline$ (A) $80h + 2 = 72h + 4$ $\newline$ (B) $80 + 2h = 72 + 4h$ $\newline$ How long did it take for the cities to reach the same temperature? $\newline$ Simplify any fractions. $\newline$ $\_\_\_$ hours $\newline$

Full solution

Q. One morning in Austin, Texas, the temperature was

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

and rose by

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

per hour until midafternoon. At the same time in Little Rock, Arkansas, the temperature was

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

and rose by

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

per hour.

\newline

Which equation can you use to find

h

, the number of hours it took for the cities to reach the same temperature?

\newline

Choices:

\newline

(A)

80h + 2 = 72h + 4

\newline

(B)

80 + 2h = 72 + 4h

\newline

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

\newline

Simplify any fractions.

\newline

\_\_\_

hours

\newline

Identify Equation: Step $1$ : Identify the correct equation to represent the situation. $\newline$ Austin's temperature starts at $80 \, ^{\circ}\mathrm{F}$ and increases by $2 \, ^{\circ}\mathrm{F}$ each hour. Little Rock's temperature starts at $72 \, ^{\circ}\mathrm{F}$ and increases by $4 \, ^{\circ}\mathrm{F}$ each hour. We need to find when the temperatures are equal, so we set up the equation: $\newline$ $80 + 2h = 72 + 4h$
Solve for h: Step $2$ : Solve for h. $\newline$ First, subtract $2h$ from both sides to get: $\newline$ $80 = 72 + 2h$
Continue Solving: Step $3$ : Continue solving for $h$ . $\newline$ Next, subtract $72$ from both sides: $\newline$ $8 = 2h$
Divide to Isolate $h$ : Step $4$ : Divide both sides by $2$ to isolate $h$ . $\newline$ $h = \frac{8}{2}$