Discussion
A tank initially holds 50 kilograms of salt in 500 litres. Pure water enters at 5 litres per minute and the well-mixed solution leaves at the same rate. What is the salt content after 100 minutes?
Answer: B
Correct answer: about 18.4 kilograms
With pure water entering and well-mixed liquid leaving at the same rate, the salt decays exponentially: \[ m = m_0e^{-t/\tau}, \qquad \tau = \frac{V}{\dot{V}} = \frac{500}{5} = 100\ \mathrm{min}. \] At \( t=\tau \) that gives \( 50e^{-1} = 18.4 \) kg. The 31.6 offered is the amount *removed* rather than the amount left, and the volume stays at 500 litres throughout because the flows balance.
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