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ææ£éé¢: \( 0.30 imes 70 = 21 \) - Silent Sales Machine

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 A tank initially contains 200 liters of water with 10 kg of dissolved salt. Saltwater with a concentration of 0.1 kg/L is pumped in at 5 L/min, while the well-mixed solution drains at 5 L/min. How much salt will remain after 30 minutes?

📌 Initial conditions: 10 kg of salt in 200 L → concentration = \( \frac{10}{200} = 0.05 \) kg/L.

📌 Inflow: \( 0.1 \, \text{kg/L} \times 5 \, \text{L/min} = 0.5 \, \text{kg/min} \).

📌 Outflow: \( \frac{V(t)}{200} \times 0.1 \times 5 \, \text{L/min} = \frac{0.5V(t)}{200} \).

📌 Let \( S(t) \) be the salt in kg at time \( t \).

📌 The differential equation is \( \frac{dS}{dt} = 0.5 - \frac{0.5S}{200} \).

📌 Solving gives \( S(t) = 10e^{-0.0025t} + 20(1 - e^{-0.0025t}) \).

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