A tank contains 70 gallons of pure water. A brine solution with 2 lbs/gal of salt enters at 2.25 gal/min and the well - stirred mixture leaves at the same rate. Find the amount of salt in the tank at any time and the time at which the brine leaving the tank will contain 15 lbs of salt.

York 2021-01-19 Answered
A tank contains 70 gallons of pure water. A brine solution with 2 lbs/gal of salt enters at 2.25 gal/min and the well - stirred mixture leaves at the same rate. Find the amount of salt in the tank at any time and the time at which the brine leaving the tank will contain 15 lbs of salt.
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Expert Answer

delilnaT
Answered 2021-01-20 Author has 94 answers

Form a differential equation that solves the amount of salt at any time t as follows
dAdt= rate in - Rate out
=22.25A(t)702.25
=4.59A(t)/280
=12609A280
dAdt=12609A280, A(0)= 0
dA12609A=dt280
dA12609A=dt280
19ln(12609A)=t280+C
A(0)= 0
C=19ln(1260)
ln(12609A)=9t280+ln(1260)
12609A=e9t280+ln(1260)
12609A=1260e9t280
140A=140e9t280
A(t)=140140e9t280
Obtain the time at which the brine leaving the tank will contain 15 lbs of salt as follows
A(t)=140140e9t280
15=140140e9t280
140e9t280=14015
e9t280=125140
9t280=ln(125140)
t=2809ln(125140)
t=3.53min

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