You've lost your dinner jacket in a palace with 1,514 doors, and it could be anywhere. how many rooms must you potentially look
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Let = amount of salt (in pounds) in the tank at time
(in minutes). Then
.
Salt flows in at a rate
and flows out at a rate
where 4 quarts = 1 gallon so 13 quarts = 3.25 gallon.
Then the net rate of salt flow is given by the differential equation
which I'll solve with the integrating factor method.
Integrate both sides. By the fundamental theorem of calculus,
After 1 hour = 60 minutes, the tank will contain
pounds of salt.