Problem. A tank initially contains 100 gallons of brine solution with concentration 2 pound of salts per gallon. Beginning at time zero, brine containing 1 pound of salt per gallon is being added to the tank at the rate of 2 gallons per minute, and the mixture is being poured out of the tank at the rate of 3 gallons per minute. Find a general function indicating the amount of salt in the tank in terms of time t. (a) Set up an initial value problem describing the amount A(t) of salts in the tank at any time. (b) Solve the initial value problem in Part (a). (c) Find the amount of salts in the tank when there are 50 gallons of brine left in the tank.
Problem. A tank initially contains 100 gallons of brine solution with concentration 2 pound of salts per gallon. Beginning at time zero, brine containing 1 pound of salt per gallon is being added to the tank at the rate of 2 gallons per minute, and the mixture is being poured out of the tank at the rate of 3 gallons per minute. Find a general function indicating the amount of salt in the tank in terms of time t. (a) Set up an initial value problem describing the amount A(t) of salts in the tank at any time. (b) Solve the initial value problem in Part (a). (c) Find the amount of salts in the tank when there are 50 gallons of brine left in the tank.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Problem. A tank initially contains 100 gallons of brine solution with concentration 2 pound
of salts per gallon. Beginning at time zero, brine containing 1 pound of salt per gallon is
being added to the tank at the rate of 2 gallons per minute, and the mixture is being poured
out of the tank at the rate of 3 gallons per minute. Find a general function indicating the
amount of salt in the tank in terms of time t.
(a) Set up an initial value problem describing the amount A(t) of salts in the tank at any
time.
(b) Solve the initial value problem in Part (a).
(c) Find the amount of salts in the tank when there are 50 gallons of brine left in the tank.
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