After finishing the prep work, Gilberta and Mar\u00eda start removing wallpaper at the same time. Gilberta removes the paper at a constant rate of 4.3m2 per hour, while Mar\u00eda removes 3.4m2 of paper per hour. Gilberta's room starts with 35m2 of paper, and Mar\u00eda's room starts with 30.5m2 of paper.Let t represent the time, in hours, since Gilberta and Mar\u00eda start removing the wallpaper.Complete the inequality to represent the times when Gilberta has more wallpaper left in her room than Mar\u00eda has in hers.tselect inequality symbolhours
Q. After finishing the prep work, Gilberta and Mar\u00eda start removing wallpaper at the same time. Gilberta removes the paper at a constant rate of 4.3m2 per hour, while Mar\u00eda removes 3.4m2 of paper per hour. Gilberta's room starts with 35m2 of paper, and Mar\u00eda's room starts with 30.5m2 of paper.Let t represent the time, in hours, since Gilberta and Mar\u00eda start removing the wallpaper.Complete the inequality to represent the times when Gilberta has more wallpaper left in her room than Mar\u00eda has in hers.tselect inequality symbolhours
Set up equations: Let's set up the equations for the amount of wallpaper left in each room after t hours. For Gilberta, the amount of wallpaper left is given by the initial amount minus the rate at which she removes it times time:Gilberta's wallpaper left = 35m2−4.3m2/h×t.For Mar\'\ia, the amount of wallpaper left is given by the initial amount minus the rate at which she removes it times time:Mar\'\ia's wallpaper left = 30.5m2−3.4m2/h×t.
Find inequality: We want to find when Gilberta has more wallpaper left than Mar\'{i}a. This means we need to find when the amount of wallpaper left in Gilberta's room is greater than the amount left in Mar\'{i}a's room: 35m^2 - 4.3\frac{m^2}{h} \cdot t > 30.5m^2 - 3.4\frac{m^2}{h} \cdot t.
Simplify inequality: Now, we simplify the inequality by subtracting 30.5m2 from both sides and adding h4.3m2⋅t to both sides:35m^2 - 30.5m^2 > \frac{4.3m^2}{h} \cdot t - \frac{3.4m^2}{h} \cdot t.
Perform calculations: Perform the calculations on both sides of the inequality: 4.5m^2 > 0.9\frac{m^2}{h} \cdot t.
Divide both sides: To find the inequality in terms of t, we divide both sides by 0.9m2/h:t < \frac{4.5m^2}{0.9m^2/h}.
Calculate value: Calculate the division to find the value for t:t < 5 hours. This means that Gilberta will have more wallpaper left in her room than Mar\'{\i}a for any time less than 5 hours.
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