Question

Asked Sep 14, 2019

A 400-gallon tank initially contains 100 gallons of brine containing 50 pounds of salt. Brine consisting of 1 pound of salt per gallon enters the tank at the rate of 5 gallons/second, and the well-mixed brine in the tank flows out at the rate of 3 gallons/second. How much salt will the tank contain when it is full of brine?

Step 1

Formulate a differential equation as follows. Let *A*(*t*) be the rate of change of amount of salt in the tank at time* t.* Also observe that:

Rate of change of *A* = Rate of input – Rate of output.

Step 2

Solve the obtained differentia...

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