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Consider the two tanks shown in the figure below. Each has a capacity of 300 gallons. At time t = 0, tank 1 contains 100 gallons of a brine solution and tank 2 contains 200 gallons of a brine solution. Each tank also initially contains 50 pounds of salt. Pure water flows into tank 1, then, a well-mixed solution flows out from tank 1 into tank 2. Finally a well-mixed solution drains out of tank 2. The three flow rates indicated in the figure are each 5 gal/min. Tank 1, capacity = 300 gal Volume of brine = 100 gal. x(t) = amount of salt (lbs.) Tank 2, capacity = 300 gal. Volume of brine = 200 gal y(t) = amount of salt (lbs.) (a) Write a system of differential equations that describes the amount of salt, ä(t), in tank 1 and the amount of salt, y(t), in tank 2. Use the variables x and y in writing your answers below. Do not use x (t) and y(t). dx dt dy dt (b) Solve the system to find formulas for x(t) and y(t). Write your answers in terms of the variable t. x(t) y(t)

Consider the two tanks shown in the figure below. Each has a capacity of 300 gallons. At time t = 0, tank 1 contains 100 gallons of a brine solution and tank 2 contains 200 gallons of a brine solution. Each tank also initially contains 50 pounds of salt. Pure water flows into tank 1, then, a well-mixed solution flows out from tank 1 into tank 2. Finally a well-mixed solution drains out of tank 2. The three flow rates indicated in the figure are each 5 gal/min. Tank 1, capacity = 300 gal Volume of brine = 100 gal. x(t) = amount of salt (lbs.) Tank 2, capacity = 300 gal. Volume of brine = 200 gal y(t) = amount of salt (lbs.) (a) Write a system of differential equations that describes the amount of salt, ä(t), in tank 1 and the amount of salt, y(t), in tank 2. Use the variables x and y in writing your answers below. Do not use x (t) and y(t). dx dt dy dt (b) Solve the system to find formulas for x(t) and y(t). Write your answers in terms of the variable t. x(t) y(t)

Advanced Engineering Mathematics
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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Consider the two tanks shown in the figure below. Each has a capacity of 300 gallons. At time t = 0, tank 1 contains 100 gallons of a brine solution and tank 2 contains 200 gallons of a brine solution. Each tank also initially contains 50 pounds of salt. Pure water flows into tank 1, then, a well-mixed solution flows out from tank 1 into tank 2. Finally a well-mixed solution drains out of tank 2. The three flow rates indicated in the figure are each 5 gal/min. Tank 1, capacity = 300 gal. Volume of brine = 100 gal. x(t) = amount of salt (lbs.) Tank 2, capacity = 300 gal. Volume of brine = 200 gal. y(t) = amount of salt (lbs.) (a) Write a system of differential equations that describes the amount of salt, x(t), in tank 1 and the amount of salt, y(t), in tank 2. Use the variables x and y in writing your answers below. Do not use x(t) and y(t). dx dt dy dt (b) Solve the system to find formulas for x(t) and y(t). Write your answers in terms of the variable t. x(t) y(t)
Transcribed Image Text:Consider the two tanks shown in the figure below. Each has a capacity of 300 gallons. At time t = 0, tank 1 contains 100 gallons of a brine solution and tank 2 contains 200 gallons of a brine solution. Each tank also initially contains 50 pounds of salt. Pure water flows into tank 1, then, a well-mixed solution flows out from tank 1 into tank 2. Finally a well-mixed solution drains out of tank 2. The three flow rates indicated in the figure are each 5 gal/min. Tank 1, capacity = 300 gal. Volume of brine = 100 gal. x(t) = amount of salt (lbs.) Tank 2, capacity = 300 gal. Volume of brine = 200 gal. y(t) = amount of salt (lbs.) (a) Write a system of differential equations that describes the amount of salt, x(t), in tank 1 and the amount of salt, y(t), in tank 2. Use the variables x and y in writing your answers below. Do not use x(t) and y(t). dx dt dy dt (b) Solve the system to find formulas for x(t) and y(t). Write your answers in terms of the variable t. x(t) y(t)
(c) Determine the maximum amount of salt in tank 2. At what time does this occur? The maximum amount of salt in tank 2 = minutes pounds, which occurs at time =
Transcribed Image Text:(c) Determine the maximum amount of salt in tank 2. At what time does this occur? The maximum amount of salt in tank 2 = minutes pounds, which occurs at time =
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