Salt Questions

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 tank after t minutes?

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)

Rate of salt going into the tank This is ‘0’ This is expected because pure water is flowing in

Rate of salt leaving the tank

Solving

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

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?

Rate of salt going in

Rate of salt going out

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

Solution

Solution

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?

Rate of salt going in

Salt going out T volume 1000 1 1025 2 1050 t 1000 + 25t

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