A tank initially contains 400 gal of fresh water. At time t=0, a brine solution witha concentration of 0.1 lb of salt per gallon enters the tank at a rate of 1 gal/min and the well-stirred mixture flows out at a rate of 2 gal/min. (a) How long does it take for the tank to become empty? (This calculation determines the time interval on which our model is valid.) (b) How much salt is present when the tank contains 100 gal of brine?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section: Chapter Questions
Problem 18T
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A tank initially contains 400 gal of fresh water. At time t=0, a brine solution witha concentration of 0.1 lb of salt per gallon enters the tank at a rate of 1 gal/min and the well-stirred mixture flows out at a rate of 2 gal/min.

(a) How long does it take for the tank to become empty? (This calculation determines the time interval on which our model is valid.)

(b) How much salt is present when the tank contains 100 gal of brine?

Expert Solution
Step 1

We will find amount of solution after t min and then find time required to empty the tank 

To find amount of salt 1st needed to make a differential equation for amount and then solve it to get amount after t minutes .

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