Consider two brine tanks connected as shown in the figure below. Tank 1 contains x(t) pounds of salt in 100 gal of brine and tank 2 contains y(t) pounds of salt in 200 gal of brine. Thebrine in each tank is kept uniform by stirring, and brine is pumped from each tank to the other at the rates indicated. In addition, fresh water flows into tank 1 at 20 gal/min, and the brine intank 2 flows out at 20 gal/min. The salt concentrations in the two tanks are x/100 pounds per gallon and y/200 pounds per gallon, respectively. The rates of change must satisfy the systemof differential equations below. If the initial (t = 0) concentration in each brine tank is 0.75 lb/gal, solve the system for the amounts x(t) and y(t) of salt in the two tanks at time t.Click on the icon to view the figure20x'= -6x+y20y' = 6x-3yCx(t) =(Do not round until the final answer. Then round to the nearest hundredth as needed. Use integers or decimals for any numbers in the expression.)y(t) =(Do not round until the final answer. Then round to the nearest hundredth as needed. Use integers or decimals for any numbers in the expression.)

Since there is no image for flow in the tanks, i use only the given equation with initial values.

Answered: Consider two brine tanks connected as…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Consider a large vat containing sugar water that is to be made into soft drinks (see figure below). A B Suppose: The vat contains 230 gallons of liquid, which never changes. Sugar water with a concentration of 7 tablespoons/gallon flows through pipe A into the vat at the rate of 5 gallons/minute. • Sugar water with a concentration of 3 tablespoons/gallon flows through pipe B into the vat at the rate of 25 gallons/minute. The liquid in the vat is kept well-mixed. • Sugar water leaves the vat through pipe C at the rate of 30 gallons/minute. Let S(t) represent the number of tablespoons of sugar in the vat at time t, where t is given in minutes. (A) Write the DE model for the time rate of change of sugar in the vat: dS dt (B) Solve the differential equation to find the amount of sugar in the vat as a function of time. Your function will have an arbitrary constant K in it. Assume that K > 0. S(t) = (C) Suppose that there are 22 tablespoons of sugar in the vat at t = 0. How many tablespoons…
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A tank initially holding 80 gals of fuid with 40 lbs of salt has two sources of fluid being pumped in. One source is pumping pure water in at 8 gal/min and the second source is pumping in a salt solution of 0.5 Ibs/gal at 2 gal/min. The tank is emptying at 10 gal/min. Find the amount of salt in the tank after 30 minutes?
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