A tank with a capacity of 250 gal is intended to be used to prepare a sugar solution. The tank initially contains 100 gal of fresh water, in which 25 lb of sugar is dissolved. On the other hand, a sugar solution enters the tank at a rate of 5 gal/min, which contains 3 lb/gal, while the mixed solution leaves at a rate of 2 gal/min. (a) Write the differential equation and the conditions that allow to determine the amount of sugar in the tank depending on the time. (b) Determine the amount of sugar in the tank at any time t.
A tank with a capacity of 250 gal is intended to be used to prepare a sugar solution. The tank initially contains 100 gal of fresh water, in which 25 lb of sugar is dissolved. On the other hand, a sugar solution enters the tank at a rate of 5 gal/min, which contains 3 lb/gal, while the mixed solution leaves at a rate of 2 gal/min. (a) Write the differential equation and the conditions that allow to determine the amount of sugar in the tank depending on the time. (b) Determine the amount of sugar in the tank at any time t.
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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A tank with a capacity of 250 gal is intended to be used to prepare a sugar solution. The tank initially contains 100 gal of fresh water, in which 25 lb of sugar is dissolved. On the other hand, a sugar solution enters the tank at a rate of 5 gal/min, which contains 3 lb/gal, while the mixed solution leaves at a rate of 2 gal/min.
(a) Write the differential equation and the conditions that allow to determine the amount of sugar in the tank depending on the time.
(b) Determine the amount of sugar in the tank at any time t.
(c) How long will it take for the tank to contain 160 lb of sugar?
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