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Home » \frac(a + b)^2 + (a - b)^2(a - b)(a + b) = 3 - Portal da AcÃºstica

\frac(a + b)^2 + (a - b)^2(a - b)(a + b) = 3 - Portal da AcÃºstica

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 #### 13**Question 1:

📌 Alice and Bob are working on a project. Alice can complete a task in 12 hours, while Bob can complete it in 15 hours. If they work together, but Alice starts an hour later than Bob, how long will it take them to complete the task?

📌 Bob's work rate: \(\frac{1}{15}\) of the task per hour

📌 Alice's work rate: \(\frac{1}{12}\) of the task per hour

📌 Bob works alone for 1 hour: \(\frac{1}{15}\) of the task

📌 Combined work rate when both work: \(\frac{1}{12} + \frac{1}{15} = \frac{5+4}{60} = \frac{9}{60} = \frac{3}{20}\)

📌 Remaining task after 1 hour: \(1 - \frac{1}{15} = \frac{14}{15}\)

📌 Time needed to complete \(\frac{14}{15}\) at combined rate: \(\frac{14/15}{3/20} = \frac{14}{15} \times \frac{20}{3} = \frac{280}{45} = \frac{56}{9} \approx 6.22\) hours

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