Tank # 1 initially holds 50 gals of brine with a concentration of 1 lb/gal, while Tank # 2 initiallyholds 25 gals of brine with a concentration of 3 lb/gal. Pure H20 flows into Tank # 1 at 5 gal/min.The well-stirred solution from Tank # 1 then flows into Tank # 2 at 5 gal/min . The solution inTank # 2 flows out at 5 gal/min. Set up and solve an IVP that gives x1(t) and x2(t), the amountof salt in Tanks # 1 and # 2, respectively, at time t.

The working principle here will be Rate of change of salt=Inflow of salt-outflow of salt. The amount…

Answered: Tank # 1 initially holds 50 gals of…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Similar questions

A 100L-capacity tank initially holds 80L of fresh water. A brine solution is poured into the tank at the rate of 4 L/hr, while the well-stirred mixture leaves the tank at the rate of 8 L/hr. If for the first three hours, the solution being poured into the tank contains 2g/L of salt, and for the succeeding hours, the solution being poured in contains 1g/L of salt, find the amount of salt in the tank when the tank starts to overflow.
A tank contains 200 liters of brine in which there are 3 kg of salt per liter. It is desired to dilute this solution by adding brine containing 1 kg of salt per liter, which flows into the tank at the rate of 4 liters/min and the mixture, kept uniform by stirring, runs out at the same rate. When will the tank contain 1.5 kg of salt per liter?
Two large tanks, each holding 24 liters of a brine solution, are interconnected by pipesas shown in the figure. Fresh water follows into tank T1 at a rate of 6L/min and fluid is drainedout of tank T2 at the same rate; also 8L/min of fluid are pumped from tank T1 to tank T2 and2L/min from tank T2 to tank T1. The liquids inside each tank are kept well stirred. If, initially, thebrine solution in tank T1 contains 1 kg of salt and that in tank T2 contains 6 kg of salt, determinethe mass of salt in each tank at time t > 0
Consider two tanks T1 and T2 with T1 containing 50 gallons of water in which 25 pounds of salt is dissolved and T2 containing 50 gallons of pure water. Pure water flows from outside into T1 at a rate of 4 gal/min and salt solution is circulated at rates of 6 gal/min from T1 to T2 and 2 gal/min from T2 to T1. If the content of T2 is withdrawn out of the system at the same rate as the pure water to T1 (i.e., 4 gal/min) to ensure no liquid volume change in the system, and the mixture in each tank is well mixed, find the salt contents y1 (t) and y2 (t) in T1 and T2 respectively. Determine the time it would take for the salt contents in the two tanks to be equal.
20.Consider two interconnected tanks similar to those in Figure 7.1.6. Initially, Tank 1 contains 60 gal of water and Q01Q10 oz of salt, and Tank 2 contains 100 gal of water and Q02Q20 oz of salt. Water containing q1 oz/gal of salt flows into Tank 1 at a rate of 3 gal/min. The mixture in Tank 1 flows out at a rate of 4 gal/min, of which half flows into Tank 2, while the remainder leaves the system. Water containing q2 oz/gal of salt also flows into Tank 2 from the outside at the rate of 1 gal/min. The mixture in Tank 2 leaves it at a rate of 3 gal/min, of which some flows back into Tank 1 at a rate of 1 gal/min, while the rest leaves the system. a.Draw a diagram that depicts the flow process described above. Let Q1(t) and Q2(t), respectively, be the amount of salt in each tank at time t. Write down differential equations and initial conditions for Q1 and Q2 that model the flow process. b.Find the equilibrium values QE1Q1E and QE2Q2E in terms of the concentrations q1 and q2. c.Is it…
The radiator in a car is filled with a solution of 55% antifreeze and 45% water. The manufacturer of the antifreeze suggests that for summer driving, optimal cooling of the engine is obtained with only 50% antifreeze. If the capacity of the radiator is 3.3 L, how much coolant should be drained and replaced with water to reduce the antifreeze concentration to the recommended level?
A 200 gallon tank initially contains 100 gallons of water with 20 pounds of salt. A salt solution with 1/4 pound of salt per gallon is added to the tank at 4 gal/min, and the resulting mixture is drained out at 2 gal/min. Find the quantity of salt in the tank as it's about to overflow.
A 200-gal tank is half full of distilled water.At time t = 0, a solution containing 0.5 lb / gal of concentrate entersthe tank at the rate of 5 gal/ min, and the well-stirred mixtureis withdrawn at the rate of 3 gal / min. At what time will the tank be full?

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