Priya wants to buy a new litter box that has the same volume as her old one. Her former rectangular litter box measured inches on the base and was 4 inches tall. If her new rectangular litter box has a base with a length and width that are exactly 50 percent longer than the corresponding length and width of the base of the former litter box, to the nearest tenth of an inch approximately how many inches tall will the new litter box be?

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The ACT Mathematics Test contains 60 questions to be answered in 60 minutes.  The hardest ACT math questions (the last 10 to 15 questions) fall into two types: advanced concepts and complex questions. Advanced concepts questions cover what you learn in precalculus and trigonometry. FYI: Students that get into Harvard College have an ACT score of 34–36.

Priya wants to buy a new litter box that has the same volume as her old one. Her former rectangular litter box measured <img alt='images' src='https://www.fatskills.com/images2/ACT/eq02298.png'/><!--<m:math display='inline' overflow='scroll' xmlns:m='http://www.w3.org/1998/Math/MathML'><m:mrow><m:mn>12</m:mn><m:mo>×</m:mo><m:mn>24</m:mn></m:mrow></m:math>--> inches on the base and was 4 inches tall. If her new rectangular litter box has a base with a length and width that are exactly 50 percent longer than the corresponding length and width of the base of the former litter box, to the nearest tenth of an inch approximately how many inches tall will the new litter box be?