To find out how long it will take Stacy to paint the entire bedroom, we first determine her painting rate. She paints \(\frac{3}{4}\) of the bedroom in 3 hours.
To find the time it takes to paint the entire bedroom, we can set up a proportion based on her current rate:
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First, find the time it takes to paint just \(\frac{1}{4}\) of the bedroom: \[ \text{Time for } \frac{1}{4} = \frac{3 \text{ hours}}{\frac{3}{4}} = 3 \times \frac{4}{3} = 4 \text{ hours} \]
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To paint the entire bedroom, she will take: \[ \text{Total time} = 3 \text{ hours} + 4 \text{ hours} = 4 \text{ hours} + 3 \text{ hours} = 4 \text{ hours} \]
Alternatively, we can also use the formula related to rates:
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If she paints \(\frac{3}{4}\) in 3 hours, then her painting rate is: \[ \text{Rate} = \frac{\frac{3}{4}}{3 \text{ hours}} = \frac{1}{4} \text{ of the bedroom per hour} \]
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To paint the entire bedroom (1 full unit), it would take: \[ \text{Time} = \frac{1 \text{ full bedroom}}{\frac{1}{4} \text{ bedroom per hour}} = 4 \text{ hours} \]
Therefore, it will take Stacy 4 hours to paint the entire bedroom.
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