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Salt Questions

This problem involves a series of questions related to the dynamics of salt concentration in brine tanks. The scenarios examine the rates of salt entering and leaving the tanks, the initial and subsequent concentrations of salt, and how these factors change over time. Specifically, we analyze how much salt remains in a tank under varying conditions, detailing calculations based on flow rates of both saltwater and pure water. Ultimately, the goal is to express these changes as functions of time and understand the flow dynamics within the system.

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Salt Questions

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  1. Salt Questions

  2. Question 1 A tank contains 1000 litres of brine with 15kg of dissolved salt. Pure water enters the tank at a rate of 10 litres/min. The solution is kept thoroughly mixed and drains from the tank at the same rate. How much salt is in the tankafter t minutes?

  3. Define the function s(t) = kg of salt in the tank at time t minutes This is what we are looking for. S’(t) = the rate at which the amount of salt in the tank is changing = (rate of salt going in) - (rate of salt going out)

  4. Rate of salt goinginto the tank • This is ‘0’ • This is expected because pure water is flowing in

  5. Rate of salt leaving the tank

  6. Solving

  7. When t = 0, 15kg of dissolved salt was in the tank.

  8. Question 2 A tank contains 1000 litres of pure water. Brine that contains 0.05 kg of salt per litre enters the tank at a rate of 5 litres/min. Brine that contains 0.04 kg of salt per litre enters the tank at the rate of 10 litres/min. The solution is kept thoroughly mixed and drains from the tank at 15 litres/min. How much salt is left in the tank after t mins?

  9. Rate of salt going in

  10. Rate of salt going out

  11. Rate of change (Rate going in) – (Rate going out)

  12. Solution

  13. Solution

  14. Question 3 Into a 2000 litre container is placed 1000 litres of a brine solution containing 40 kg of salt. A brine solution containing 0.02 kg/l of salt flows into the container at a rate of 50 l/min. The solution is kept thoroughly mixed, and the mixture flows out at a rate of 25 l/min. How much salt is in the container at the moment it overflows?

  15. Rate of salt going in

  16. Salt going out

  17. The variables are not separable and hence another technique is required (not in the curriculum)

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