Consider the two tanks shown in the figure below. Each has a capacity of 300 gallons. At time t = 0, tank 1contains 100 gallons of a brine solution and tank 2 contains 200 gallons of a brine solution. Each tank alsoinitially contains 50 pounds of salt. Pure water flows into tank 1, then, a well-mixed solution flows outfrom tank 1 into tank 2. Finally a well-mixed solution drains out of tank 2. The three flow rates indicated inthe figure are each 5 gal/min.Tank 1, capacity = 300 gal.Volume of brine =100 gal.x(t) = amount of salt (Ibs.)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, r(t), in tank 1 and theamount of salt, y(t), in tank 2. Use the variables a and y in writing your answers below. Do not use x(t)and y(t).dadtfipdt(b) Solve the system to find formulas for x(t) and y(t). Write your answers in terms of the variable t.z(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 =pounds, which occurs at timeminutes||

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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 (Ibs.) (a) Write a system of differential equations that describes the amount of salt, r(t), in tank 1 and the amount of salt, y(t), in tank 2. Use the variables a and y in writing your answers below. Do not use r(t) and y(t). da dt dy dt (b) Solve the system to find formulas for a(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 = pounds, which occurs at time minutes

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 (Ibs.) (a) Write a system of differential equations that describes the amount of salt, r(t), in tank 1 and the amount of salt, y(t), in tank 2. Use the variables a and y in writing your answers below. Do not use r(t) and y(t). da dt dy dt (b) Solve the system to find formulas for a(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 = pounds, which occurs at time minutes

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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Question

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 (Ibs.)
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, r(t), in tank 1 and the
amount of salt, y(t), in tank 2. Use the variables a and y in writing your answers below. Do not use x(t)
and y(t).
da
dt
fip
dt
(b) Solve the system to find formulas for x(t) and y(t). Write your answers in terms of the variable t.
z(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 =
pounds, which occurs at time
minutes
||

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