A large tank holds 400 gallons of salt water. A salt water solution with concentration 2 lb/gal is being pumped into the tank at a rate of 3 gal/min. The tank is simultaneously being emptied at a rate of 1 gal/min. If 100 pounds of salt was dissolved in the tank initially, how much salt is in the tank after 250 minutes?

So the tank contains 1866.67 lbs of salt after 250 minutes.

Step-by-step explanation:

The tank salt concentration at any moment is given as

Now the rate of change of concentration is given as

Here

SC_in is given as 2 lb/gal

FR_in is given as 3 gal/min

SC_tank is given in above equation

FR_out is given as 1 gal/min

Putting all in the equation gives

Multiplying by the integrating factor of on both sides

Integrating both sides with respect to t gives

For the initial condition Q(0)=100 lbs so the equation is given as

So the equation is

Solving for the t=250

4

step-by-step explanation:

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x