Respuesta :
after 0.05 hours the bathroom will be warmer than the closet
Explanation
Step 1
Set the equations.
let x represents the number of hours, so
a)A bathroom has a temperature of -.5 degrees F and heats up 15 degrees F. each hour,so
[tex]\begin{gathered} \text{temperature}=-0.5+(15\text{ degr}ees\text{ per hour)} \\ T_{bathroom}=-0.5+15x\Rightarrow equation\text{ (1)} \end{gathered}[/tex]b)A closet has a temperature of -.25 degrees F. and it heats up 10 degrees F. each hour, so
[tex]\begin{gathered} \text{Temperature}_{closet}=-0.25+(10\text{ degr}ees\text{ per hour)} \\ T_{closet}=-0.25+10x\Rightarrow equation(2) \end{gathered}[/tex]Step 2
For what number of hours will the bathroom be warmer than the closet?
to solve this we need to formule an inequality
[tex]\begin{gathered} T_{bathroom}>T_{closet} \\ hence \\ -0.5+15x>-0.25+10x \end{gathered}[/tex]now, we need to solve the inequality
[tex]\begin{gathered} -0.5+15x>-0.25+10x \\ \text{subtract x in both sides} \\ -0.5+15x-10x>-0.25+10x-10x \\ 5x-.5>-0.25 \\ \text{add 0.5 in both sides} \\ 5x-.5+0.5>-0.25+0.5 \\ 5x>0.25 \\ \text{divide both sides by 5} \\ \frac{5x}{5}>\frac{0.25}{5} \\ x>0.05\text{ hours} \end{gathered}[/tex]therefore, after 0.05 hours the bathroom will be warmer than the closet
I hope this helps you
