A tank contains 400 gallons of brine (salt in solution) in which 125 pounds of salt...

A tank contains 400 gallons of brine (salt in solution) in which 125 pounds of salt has been dissolved. Freshwater (with no salt added) runs into the tank at a rate of 4 gallons per minute, and the stirred mixture is drained from the tank at the same rate. (1) Find the amount of salt in the tank after an hour. (2) How long does it take to reduce the amount of salt in the tank to 10 pounds?

Solutions

Expert Solution

milcah answered 1 year ago

Next > < Previous

Related Solutions

A tank initially contains 300 gallons of a salt solution made by dissolving 30 pounds of...

A tank initially contains 300 gallons of a salt solution made by dissolving 30 pounds of salt in water. A solution containing 0.6 pounds of salt per gallon enters the tank at a rate of 5 gallons per minute. A drain is opened at the bottom of the tank through which the well stirred solution leaves the tank at the same rate of 5 gallons per minute. Let y(t) denote the amount of salt (in pounds) which is in the...

A tank is filled to capacity with 400 gallons water containing 30 lbs of salt. Brine...

A tank is filled to capacity with 400 gallons water containing 30 lbs of salt. Brine containing 2 lbs of salt per gallon is pumped into the tank at a rate of 3 gallons per minute. The well mixed solution is pumped out at rate of 3.5 gallons per minute. Determine the differential equation of the model and solve for an equation relating amount of salt in tank at time t. Determine the time until the tank is empty.

A tank initially contains 150 gal of brine in which 20lb of salt are dissolved. A...

A tank initially contains 150 gal of brine in which 20lb of salt are dissolved. A brine containing 3 lb/gal of salt runs into the tank at the rate of 4 gal/min.The mixture is kept uniform by stirring and flows out of the tank at the rate of 3 gal/min. Let y represent the amount of salt at time t. Complete parts a through e. a. At what rate (pounds per minute) does salt enter the tank at time t?...

A 200 gallon tank initial contains 100 gallons of water and 20 pounds of dissolved salt....

A 200 gallon tank initial contains 100 gallons of water and 20 pounds of dissolved salt. Brine solution begins to enter the tank at the rate of 2 gal/min with a salt concentration of 2 lb/gal. The well mixed solution leaves the tank at the rate of 1 gal/min. Find the amount of salt inside the tank 50 minutes after the process starts?

A 100 gallon tank initially contains 10 gallons of fresh water. At t=0 a brine solution...

A 100 gallon tank initially contains 10 gallons of fresh water. At t=0 a brine solution containing 1 pound of salt per gallon is poured into the tank at the rate of 4 gal/min., while the well-stirred mixture leaves the tank at the rate of 2 gal/min. Find the amount of salt in the tank at the moment of overflow. Enter answer as numerical decimal correct to two decimal places. pounds.

1. A 100-gallon tank initially holds 50 gal of brine containing 5 pounds of salt. Brine...

1. A 100-gallon tank initially holds 50 gal of brine containing 5 pounds of salt. Brine containing 1 pound of salt per gallon enters the tank at the rate of 4 gal/s, and the well-mixed brine in the tank flows out at the rate of 3 gal/s. (a) How much salt will the tank contain at the time when the tank is full of brine? (b) If the tank had an infinite capacity, what is the maximum amount of salt...

A tank contains 365 gallons of water and 50 oz of salt. Water containing a salt...

A tank contains 365 gallons of water and 50 oz of salt. Water containing a salt concentration of 1/6(1 + 1/4 sin t) oz/gal flows into the tank at a rate of 8 gal/min, and the mixture in the tank flows out at the same rate. The long-term behavior of the solution is an oscillation about a certain constant level. a) What is this level? b) What is the amplitude of the oscillation?

A tank contains 360 gallons of water and 50 oz of salt. Water containing a salt...

A tank contains 360 gallons of water and 50 oz of salt. Water containing a salt concentration of 1 6 (1 + 1 4 sin t) oz/gal flows into the tank at a rate of 8 gal/min, and the mixture in the tank flows out at the same rate. The long-term behavior of the solution is an oscillation about a certain constant level. a) What is this level? b) What is the amplitude of the oscillation? (Round your answers to...

A tank contains 1000L of pure water. Brine that contains 0.05kg of salt per liter enters...

A tank contains 1000L of pure water. Brine that contains 0.05kg of salt per liter enters the tank at a rate of 5L/min. Also, brine that contains 0.09kg of salt per liter enters the tank at a rate of 10L/min. The solution is kept thoroughly mixed and drains from the tank at a rate of 15L/min. Answer the following questions. 1. How much salt is in the tank after t minutes? Answer (in kilograms): S(t)= 2. How much salt is...

Suppose that a large mixing tank initially holds 400 gallons of water in which 65 pounds...

Suppose that a large mixing tank initially holds 400 gallons of water in which 65 pounds of salt have been dissolved. Another brine solution is pumped into the tank at a rate of 6 gal/min, and when the solution is well stirred, it is pumped out at a slower rate of 5 gal/min. If the concentration of the solution entering is 3 lb/gal, find the amount of salt in the tank after 10 minutes. PLEASE SHOW ALL WORK AND USE...

Subjects