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Home » \[ u' = k, \quad v' = 2t \] - 500apps

\[ u' = k, \quad v' = 2t \] - 500apps

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📌 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 \( \frac{1}{6} \):

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

📌 Total time = 2 hours + \( \frac{2}{3} \) hours = \( \frac{6}{3} + \frac{2}{3} = \frac{8}{3} \) hours = 2 hours and 40 minutes.

📌 But in decimal form: \( \frac{8}{3} \approx 2.\overline{6} \), so as a single value:

📌 #### 2.67 (rounded to two decimal places)

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