A tank contains 60 kg of salt and 1000 L of water. Pure water enters a...

A tank contains 60 kg of salt and 1000 L of water. Pure water enters a tank at the rate 12 L/min. The solution is mixed and drains from the tank at the rate 6 L/min.

(a) What is the amount of salt in the tank initially?
amount =  (kg)

(b) Find the amount of salt in the tank after 3 hours.
amount =   (kg)

(c) Find the concentration of salt in the solution in the tank as time approaches infinity. (Assume your tank is large enough to hold all the solution.)
concentration =   (kg/L)

Expert Solution

The given problem is modeled in the form of an initial value problem which we have solved based on the given information. The solutions to all the questions are provided in the attachments.

Colby Messinger answered 2 years ago

A tank contains 90 kg of salt and 2000 L of water: Pure water enters a...

A tank contains 90 kg of salt and 2000 L of water: Pure water enters a tank at the rate 8 L/min. The solution is mixed and drains from the tank at the rate 4 L/min. What is the amount of salt in the tank initially? Find the amount f salt in the tank after 4.5 hours. Find the concentration of salt in the solution in the tank as the time approaches infinity. (Assume your tank is large enough to...

A tank contains 9,000 L of brine with 11 kg of dissolved salt. Pure water enters...

A tank contains 9,000 L of brine with 11 kg of dissolved salt. Pure water enters the tank at a rate of 90 L/min. The solution is kept thoroughly mixed and drains from the tank at the same rate. (a) How much salt is in the tank after t minutes? (b) How much salt is in the tank after 10 minutes? (Round your answer to one decimal place.)

A tank contains 100kg of salt and 2000L of water. Pure water enters a tank at...

A tank contains 100kg of salt and 2000L of water. Pure water enters a tank at the rate 6L/min. The solution is mixed and drains from the tank at the rate 3L/min. ) Find the concentration(kg/L) of salt in the solution in the tank as time approaches infinity. (Assume your tank is large enough to hold all the solution.)

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...

A tank contains 70 kg of salt and 2000 L of water. Water containing 0.4kg/L of...

A tank contains 70 kg of salt and 2000 L of water. Water containing 0.4kg/L of salt enters the tank at the rate 16L/min. The solution is mixed and drains from the tank at the rate 4L/min. A(t) is the amount of salt in the tank at time t measured in kilograms. (a) A(0) = (kg) (b) A differential equation for the amount of salt in the tank is =0=0. (Use t,A, A', A'', for your variables, not A(t), and move everything...

A tank contains 2340 L of pure water. A solution that contains 0.07 kg of sugar...

A tank contains 2340 L of pure water. A solution that contains 0.07 kg of sugar per liter enters a tank at the rate 9 L/min The solution is mixed and drains from the tank at the same rate. (a) How much sugar is in the tank initially? (kg) (b) Find the amount of sugar in the tank after ?t minutes. amount = (kg) (your answer should be a function of ?t) (c) Find the concentration of sugar in the solution...

A tank contains 2140 L of pure water. A solution that contains 0.01 kg of sugar...

A tank contains 2140 L of pure water. A solution that contains 0.01 kg of sugar per liter enters a tank at the rate 6 L/min. The solution is mixed and drains from the tank at the same rate. (a) How much sugar is in the tank initially? (b) Find the amount of sugar in the tank after t minutes. (c) Find the concentration of sugar (kg/L) in the solution in the tank after 51 minutes.

A tank contains 2800 L of pure water. A solution that contains 001 kg of sugar...

A tank contains 2800 L of pure water. A solution that contains 001 kg of sugar per liter enters a tank at the rate 9 L/min The solution is mixed and drains from the tank at the same rate. a) How much sugar is in the tank initially? b) Find the amount of sugar in the tank after t minutes. amount = (kg) (your answer should be a function of t) c) Find the concentration of sugar in the solution...

A tank initially contains 80gal of pure water. Brine containing 2lb of salt per gallon enters...

A tank initially contains 80gal of pure water. Brine containing 2lb of salt per gallon enters the tank at 2gal/min, and the (perfectly mixed) solution leaves the tank at 3 gal/min. Thus the tank is empty after exactly 80 min. (A) Find the amount of salt in the tank after t minutes. (b) What is the maximum amount of salt ever in the tank?

A tank contains 220 L of pure water. Solution that contains 0.08 kg of sugar per...

A tank contains 220 L of pure water. Solution that contains 0.08 kg of sugar per liter enters the tank at the rate 8 L/min, and is thoroughly mixed into it. The new solution drains out of the tank at the same rate. (a) How much sugar is in the tank at the begining? y(0)=___ kg (b) Find the amount of sugar after t minutes. y(t)=___ kg (c) As t becomes large, what value is y(t) approaching ? In other...

Question