Two tanks are connected as in the figure below. Tank 1 initially contains 20 pounds of salt dissolved in 100 gallons of brine. Tank 2 initially contains 150 gallons of brine in which 90 pounds of salt are dissolved. At time zero, a brine solution containing 1/2 pound of salt per gallon is added to Tank 1 at the rate of 5 gallons per minute. Tank 1 has an output that discharges brine into Tank 2 at the rate of 5 gallons per minute, and Tank 2 also has an output of 5 gallons per minute. a) Determine the amount of salt in EACH tank at any time t.HINT: Solve for the amount of salt in Tank 1 at time t, and use this solution to help determine the amount of salt in Tank 2.b) Find the time when the concentration of salt in the second tank is a minimum and its corresponding concentration.c) Determine the limiting value for the amount of salt in EACH tank after a very long time. Two tanks are connected as in the figure below. Tank 1 initially contains 20 pounds of salt dissolved in 100gallons of brine. Tank 2 initially contains 150 gallons of brine in which 90 pounds of salt are dissolved. At timezero, a brine solution containing 1/2 pound of salt per gallon is added to Tank 1 at the rate of 5 gallons perminute. Tank 1 has an output that discharges brine into Tank 2 at the rate of 5 gallons per minute, and Tank 2also has an output of 5 gallons per minute.4.5 gal/min; 1/2 lb/gal5 gal/minTank 1Tank 25 gal/mina) Determine the amount of salt in EACH tank at any time t.HINT: Solve for the amount of salt in Tank 1 at time t, and use this solution to help determine theamount of salt in Tank 2.b) Find the time when the concentration of salt in the second tank is a minimum and its correspondingconcentration.c) Determine the limiting value for the amount of salt in EACH tank after a very long time.

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Answered: Two tanks are connected as in the…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 15EQ

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Two tanks are connected as in the figure below. Tank 1 initially contains 20 pounds of salt dissolved in 100 gallons of brine. Tank 2 initially contains 150 gallons of brine in which 90 pounds of salt are dissolved. At time zero, a brine solution containing 1/2 pound of salt per gallon is added to Tank 1 at the rate of 5 gallons per minute. Tank 1 has an output that discharges brine into Tank 2 at the rate of 5 gallons per minute, and Tank 2 also has an output of 5 gallons per minute.

a) Determine the amount of salt in EACH tank at any time t.
HINT: Solve for the amount of salt in Tank 1 at time t, and use this solution to help determine the amount of salt in Tank 2.
b) Find the time when the concentration of salt in the second tank is a minimum and its corresponding concentration.
c) Determine the limiting value for the amount of salt in EACH tank after a very long time.