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📅 May 17, 2026 👤 scraface

May 17, 2026

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📌 A tank can be filled by Pipe A in 4 hours and by Pipe B in 6 hours. If both pipes are opened together, but Pipe B is closed after 2 hours, how long will it take to fill the tank?

📌 Rate of Pipe A = \( \frac{1}{4} \) of the tank per hour

📌 Rate of Pipe B = \( \frac{1}{6} \) of the tank per hour

📌 When both are open for 2 hours, they fill:

📌 \[ 2 \left( \frac{1}{4} + \frac{1}{6} \right) = 2 \left( \frac{3}{12} + \frac{2}{12} \right) = 2 \times \frac{5}{12} = \frac{10}{12} = \frac{5}{6} \text{ of the tank} \]

📌 Remaining tank to fill = \( 1 - \frac{5}{6} = \frac{1}{6} \)

📌 Now, only Pipe A is open, filling at \( \frac{1}{4} \) per hour. Time to fill the remaining \( \frac{1}{6} \):

📌 \[ \text{Time} = \frac{\frac{1}{6}}{\frac{1}{4}} = \frac{1}{6} \times 4 = \frac{4}{6} = \frac{2}{3} \text{ hours} \]

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