Math/Physics

posted by .

Please check my work below and comment.

A tank initially contains 80 gallons of fresh water. A 10% acid solution flows into the tank at the rate of 3 gallons per minute. The well-stirred mixture flows out of the tank at the rate of 3 gallons per minute. Find the amount of acid in the tank at the end of any time t. How much acid will be in the tank in 30 minutes? What will be the concentration (%) of acid in the tank after 30 minutes?

solution=0.3 gallons acid + 2.7 gallons H20

dy/dt = (rate in) - (rate out)
rate in = (0.3)(3) = 0.9 gallons/min
<-would this be gallons per min?

rate out = ((y(t))/80) * 3 gal/min
rate out = y(t)/(80/3)

dy/dt=(0.9)-(y(t))/(80/3)
dy/dy=((773/30)-y(t))/(80/3)

Separate into two intergrals:
Integral(dy/((773/30)-y)=Integral(dt/(80/3))
-ln|(773/30)-y| = 3t/80+C, C=-ln|773/30|
-ln|(773/30)-y|=3t/80 - ln|773/30|
y(t)=(773/30)-(773/30)e^(-3t/80)

Is this the correct equation?

Then at 30 minutes, y(30) would be 17.4 gallons acid

Percentage after 30 minutes=17.4/80
=21.8% acid???

Thanks.

correct procedure, however, one question: how did you get rate in .3*3? Wasn't it ten percent?

ah yes. Thank you!

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Math

    Beginning with a tank containing 8075 gallons of gasoline, more gas is added at a rate of 5 gallons per minute, while alcohol is added at a rate of 10 gallons per minute. When the mixture is 10% alcohol, how many gallons of the mixture …
  2. math

    Water is Pumped into an underground tank at a constant rate of 8 gallons per minute.Water leaks out of the tank at the rate of (t+1)^½ gallons per minute, for 0<t<120 minutes. At time t=0, the tank contains 30 gallons of water. …
  3. calculus

    Water is Pumped into an underground tank at a constant rate of 8 gallons per minute.Water leaks out of the tank at the rate of (t+1)^½ gallons per minute, for 0<t<120 minutes. At time t=0, the tank contains 30 gallons of water. …
  4. math

    A tank contains 50 gallons of a solution composed of 90% water and 10% alcohol. A second solution containing 50% water and 50% alcohol is added to the tank at rate of 4 gallons per minute. As the second solution is being added, the …
  5. linear

    Suppose that we have a system consisting of two interconnected tanks, each containing a brine solution. Tank A contains x(t) pounds of salt in 200 gallons of brine, and tank B contains y(t) pounds of salt in 300 gallons of brine. The …
  6. linear algebra

    Suppose that we have a system consisting of two interconnected tanks, each containing a brine solution. Tank A contains x(t) pounds of salt in 200 gallons of brine, and tank B contains y(t) pounds of salt in 300 gallons of brine. The …
  7. CALC

    A 200-gallon tank is currently half full of water that contains 50 pounds of salt. A solution containing 1 pounds of salt per gallon enters the tank at a rate of 6 gallons per minute, and the well-stirred mixture is withdrawn from …
  8. calculus

    500-gallon tank initially contains 200 gallons of brine containing 100 pounds of dissolved salt. Brine containing 2 pounds of salt per gallon flows into the tank at the rate of 4 gallons per minute, and the well-stirred mixture flows …
  9. Algebra

    A tank contains 150 gallons of water and fills at a rate of 8 gallons per minute. A second tank contains 600 gallons of water and drains at a rate of 10 gallons per minute. After how many minutes will both tanks have the same amount …
  10. Calc AB

    I've been trying to solve this problem for the past 45 minutes and could really use some help. I'm given that water flows into a tank at a rate of (5t+4) gallons/min. Water flows out of the tank at a rate of 0.5(t^2) gallons/min. At …

More Similar Questions