Question

A tank is filled with 10 gallons of brine in which is dissolved 5 lb of...

A tank is filled with 10 gallons of brine in which is dissolved 5 lb of salt. Brine containing 3 lb of salt per gallon enters the tank at a rate of 2 gal per minute, and the well-stirred mixture is pumped out at the same rate. (a) Find the amount of salt in the tank at any time t. (b) How much salt is in the tank after 10 minutes? (c) How much salt is in the tank after a long time?

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Using differential equation: A 200- gallon tank initially contains 40 gallons of brine in which 10...
Using differential equation: A 200- gallon tank initially contains 40 gallons of brine in which 10 pounds of salt have been dissolved. Starting at t=0 , brine containing 5 pounds of salt per gallon flows into the tank at rate of 6 gallons per minutes. At the same time, the well-stirred mixture flows out of the tank at the slower rate of 4 gallons per minute. a)How much salt is in the tank at the end of t minutes? b)...
A large tank is filled with 80 gallons of fluid in which 2 pounds of salt...
A large tank is filled with 80 gallons of fluid in which 2 pounds of salt are dissolved. Brine containing 1/2 pound of salt per gallon is pumped into the tank at a rate of 3 gal/min. The well-mixed solution is then pumped out at the same rate of 3 gal/min. Find the concentration of salt in the tank after 30 minutes.
A large tank contains 800 gal of water in which 42 lb of salt are dissolved....
A large tank contains 800 gal of water in which 42 lb of salt are dissolved. Brine containing 2 lb of of dissolved salt per gal is pumped into the tank at a rate of 4 gal per minute, and the mixture, kept uniform by stirring, is pumped out at the same rate. (a) Find the amount x(t) of salt in the tank, at time t. (b) How long will it take for the amount of salt in the tank...
A tank contains 40 lb of salt dissolved in 400 gallons of water. A brine solution...
A tank contains 40 lb of salt dissolved in 400 gallons of water. A brine solution is pumped into the tank at a rate of 4 gal/min; it mixes with the solution there, and then the mixture is pumped out at a rate of 4 gal/min. Determine A(t), the amount of salt in the tank at time t, if the concentration of salt in the inflow is variable and given by cin(t) = 2 + sin(t/4) lb/gal.
A tank contains 70 lb of salt dissolved in 200 gallons of water. A brine solution...
A tank contains 70 lb of salt dissolved in 200 gallons of water. A brine solution is pumped into the tank at a rate of 2 gal/min; it mixes with the solution there, and then the mixture is pumped out at a rate of 2 gal/min. Determine A(t), the amount of salt in the tank at time t, if the concentration of salt in the inflow is variable and given by cin(t) = 2 + sin(t/4) lb/gal.
A tank contains 30 gallons of brine solution containing 10 lb of salt. Another brine solution...
A tank contains 30 gallons of brine solution containing 10 lb of salt. Another brine solution of concentration of 3 lb/gallon is poured into the tank at the rate of 2 gallons/min. The well stirred solution in the tank is drained out at the rate of 2 gallons/min. Let the amount of salt in the tank at time ? be ?(?). Write the differential equation for A(t) and solve it.
A 110 gallon tank initially contains 5 lbs salt dissolved in 60 gallons of water. Brine...
A 110 gallon tank initially contains 5 lbs salt dissolved in 60 gallons of water. Brine containing 1 lb salt per gallon begins to flow into the tank at the rate of 3 gal/min and the well-mixed solution is drawn off at the rate of 1 gal/min. How much salt is in the tank when it is about to overflow? (Round your answer to the nearest integer.)
A 500​-gal tank initially contains 100 gal of brine containing 75 lb of salt. Brine containing...
A 500​-gal tank initially contains 100 gal of brine containing 75 lb of salt. Brine containing 2 lb of salt per gallon enters the tank at a rate of 5 ​gal/s, and the​ well-mixed brine in the tank flows out at the rate of 3 ​gal/s. How much salt will the tank contain when it is full of​ brine?
A 100 gallon tank is filled with brine solution containing 50 pounds of salt. Pure water...
A 100 gallon tank is filled with brine solution containing 50 pounds of salt. Pure water enters the tank a rate of 10 gal per hour. Well mixed solution leaves the first tank at the same rate (10 gal/hr) and enters a second 100 gallon tank initially containing 10 pounds of salt. How much salt is in tank 2 at any time?
A tank initially contains 150 gal of brine in which 60 lb of salt are dissolved....
A tank initially contains 150 gal of brine in which 60 lb of salt are dissolved. A brine containing 4 ​lb/gal of salt runs into the tank at the rate of 6 ​gal/min. The mixture is kept uniform by stirring and flows out of the tank at the rate of 5 ​gal/min. Let y represent the amount of salt at time t. Complete parts a through f. a. At what rate​ (pounds per​ minute) does salt enter the tank at...