A tank contains 80 kg of salt and 1000 L of water A solution

A tank contains 80 kg of salt and 1000 L of water. A solution of a concentration 0.04 kg of salt per liter enters a tank at the rate 7 L/min. The solution is mixed and drains from the tank at the same rate. What is the concentration of our solution in the tank initially? Concentration = Find the amount of salt in the tank after 2.5 hours, amount = Find the concentration of salt in the solution in the tank as time approaches infinity, concentration =

Solution

1.
Initial concentration = 80/1000 = 0.08kg/liter

2.
After 2.5 hours quantity of liquid entered
= 7 *150 = 1050 litres
and
quantity of salt = 1050 * 0.04 = 42 kg

Now ratio of old liquid to new liquid = 1000: 1050 = 20:21

Also 1050 litres of liquid has been drained
Then
Qty remaining of each liquid is
1000 *20/41 and 1050 * 20/41

Qty of salt
= 1000*20/41*0.08 + 1050*20/41*0.04
= (2000 + 1050)20/41 *0.04
= 59 kgs of salt

3.
As time approaches infinity concentration will aproach 0.04kg/liter