A water tank contains $500$ litres of a solution with $15$ kilograms of dissolved salt. Pure wat

Question

A water tank contains $500$ litres of a solution with $15$ kilograms of dissolved salt. Pure water enters the tank at a rate of $20$ litres per minute. The solution is drained from the tank at the same rate. Let $x$ kg be the amount of salt in the tank at time $t$ minutes. Show that $\frac{\mathrm{d}x}{\mathrm{d}t}=-\frac{x}{25}$ [1] State an assumption required for this model to be more appropriate. [1] Find the amount salt in the tank after $30$ minutes. [4]

Accepted Answer

(i) $\frac{\mathrm{d}x}{\mathrm{d}t} = -\frac{x}{25}$ (ii) Thoroughly mixed; $x = 4.52$ kg

2013 NJC P1 Q9

2013 NJC P1 Q9

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