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Terrence was filling the new fish aquariums where he works. He was able to fill [tex]1 \frac{1}{3}[/tex] aquariums in [tex]2 \frac{1}{2}[/tex] hours. At this rate, how long will it take him to fill 4 aquariums?
A. [tex]5 \frac{1}{3}[/tex] hours B. 6 hours C. [tex]7 \frac{1}{2}[/tex] hours D. 10 hours
To determine how long it will take Terrence to fill 4 aquariums, given that he can fill [tex]\(1 \frac{1}{3}\)[/tex] aquariums in [tex]\(2 \frac{1}{2}\)[/tex] hours, we can follow these steps:
1. Convert the mixed numbers to improper fractions: - [tex]\(1 \frac{1}{3} = \frac{4}{3}\)[/tex] aquariums - [tex]\(2 \frac{1}{2} = \frac{5}{2}\)[/tex] hours
2. Calculate the rate at which Terrence fills the aquariums: [tex]\[
\text{Rate} = \frac{\text{Aquariums filled}}{\text{Time taken}} = \frac{\frac{4}{3} \text{ aquariums}}{\frac{5}{2} \text{ hours}}
\][/tex]
3. To simplify the fraction for the rate, we can multiply by the reciprocal of the denominator: [tex]\[
\text{Rate} = \frac{4}{3} \div \frac{5}{2} = \frac{4}{3} \times \frac{2}{5} = \frac{8}{15} \text{ aquariums per hour}
\][/tex]
4. Determine how long it will take him to fill 4 aquariums: [tex]\[
\text{Time to fill 4 aquariums} = \frac{4 \text{ aquariums}}{\text{Rate}} = \frac{4 \text{ aquariums}}{\frac{8}{15} \text{ aquariums per hour}} = 4 \times \frac{15}{8} = \frac{60}{8} = 7.5 \text{ hours}
\][/tex]
Therefore, it will take Terrence [tex]\(7 \frac{1}{2}\)[/tex] hours to fill 4 aquariums. So, the correct option is:
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