A tank contains 90 kg of salt and 2000 L of water A solution

A tank contains 90 kg of salt and 2000 L of water. A solution of a concentration 0.0225 kg of salt per liter enters a tank at the rate 5 L/mm. The solution is mixed and drains from the tank at the same rate. What is the concentration of our solution in the tank initially? Find the amount of salt in the tank after 4.5 hours. Find the concentration of salt in the solution in the tank as time approaches infinity.

Solution

initially the tank has 90 kg of salt an 2000 L of water .

=> a> the concentation of our solution initially is = (weight of salt in kg) / (volume of water in liters)

=> C = 90/2000 = 0.045 kg / L

b>

the solution enters the tank a a rate of = 5 L /min

and the concentration of the solution is = .0225 kg/L

After 4.5 hours(270 minutes) quantity of liquid entered
= 5 * 4.5 = 5*270 = 1350 litres
and
quantity of salt = 1350 * 0.0225 = 30.375 kg

Now ratio of old liquid to new liquid = 2000: 1350 = 40:27

Also 1350 litres of liquid has been drained
Then
Quantity remaining of each liquid is
2000 *40/27 and 1350 * 40/27

Quantity of salt

= 2000*40/27*0.045 + 1350*40/27*0.0225
= 178.33 kgs of salt

amount = 178.33 kg

c> As time approaches infinity concentration will aproach = 0.0225 kg/liter