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2013 NJC P1 Q9

2013 NJC P1 Q9

6 marks
Prelims

  1. 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.

    1. Show that \(\frac{\mathrm{d}x}{\mathrm{d}t}=-\frac{x}{25}\)

      [1]

    2. State an assumption required for this model to be more appropriate.

      [1]

    Find the amount salt in the tank after \(30\) minutes.

    [4]

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

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