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]

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

Problem 1RQ

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

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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