A tank initially contains 50 gal of pure water. A salt solution containing 2 pounds of salt per gallon of water is poured into the tank at a rate of 3 gal/min. The mixture is stirred and is drained out of the tank at a rate of 3 gal/min. The mixture is stirred and is drained out of the tank at the same rate. (a) Find the initial-value problem that describes the amount Q of salt in the tank at any time. (b) Find the amount of salt in the tank at any time. (c) Find the amount of salt in the tank after 20 minutes. (d) Find the amount of salt in the tank after a long time. [3.1]

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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A tank initially contains 50 gal of pure water. A salt solution
containing 2 pounds of salt per gallon of water is poured into the
tank at a rate of 3 gal/min. The mixture is stirred and is drained out
of the tank at a rate of 3 gal/min. The mixture is stirred and is
drained out of the tank at the same rate.
(a) Find the initial-value problem that describes the amount Q of
salt in the tank at any time.
(b) Find the amount of salt in the tank at any time.
(c) Find the amount of salt in the tank after 20 minutes.
(d) Find the amount of salt in the tank after a long time.
[3.1]
Transcribed Image Text:A tank initially contains 50 gal of pure water. A salt solution containing 2 pounds of salt per gallon of water is poured into the tank at a rate of 3 gal/min. The mixture is stirred and is drained out of the tank at a rate of 3 gal/min. The mixture is stirred and is drained out of the tank at the same rate. (a) Find the initial-value problem that describes the amount Q of salt in the tank at any time. (b) Find the amount of salt in the tank at any time. (c) Find the amount of salt in the tank after 20 minutes. (d) Find the amount of salt in the tank after a long time. [3.1]
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