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 minutesThis 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 outT volume0 10001 10252 1050t 1000 + 25t

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