Question

after finishing the prep work, gilberta and maría start removing wallpaper at the same time. gilberta removes the paper at a constant rate of $4.3\\,\text{m}^2$ per hour, while maría removes $3.4\\,\text{m}^2$ of paper per hour. gilbertas room starts with $35\\,\text{m}^2$ of paper, and marías room starts with $30.5\\,\text{m}^2$ of paper. let $t$ represent the time, in hours, since gilberta and maría start removing the wallpaper. complete the inequality to represent the times when gilberta has more wallpaper left in her room than maría has in hers. $t$ select inequality symbol $\vee$ $\square$ hours show calculator

Explanation:

Step1: Define remaining wallpaper

Gilberta's remaining: $35 - 4.3t$
María's remaining: $30.5 - 3.4t$

Step2: Set up inequality

We want Gilberta's remaining > María's remaining:
$35 - 4.3t > 30.5 - 3.4t$

Step3: Isolate t terms

Subtract 30.5, add $4.3t$ to both sides:
$35 - 30.5 > 4.3t - 3.4t$
$4.5 > 0.9t$

Step4: Solve for t

Divide both sides by 0.9:
$\frac{4.5}{0.9} > t$
$5 > t$ or $t < 5$

Answer:

$t < 5$ hours