Question

A tank contains 30 gallons of brine solution containing 10 lb of salt. Another brine solution of concentration of 3 lb/gallon is poured into the tank at the rate of 2 gallons/min. The well stirred solution in the tank is drained out at the rate of 2 gallons/min. Let the amount of salt in the tank at time ? be ?(?).

Write the differential equation for A(t) and solve it.

Answer #1

A 500-gallon tank initially contains 100gal of brine containing
50lb of salt. Brine containing 2lb of salt per gallon enters the
tank at the rate of 4gal per minute and the well stirred solution
leaves the tank at a rate of 8gal per minute.
(a) How long will it be before the tank is empty
(b) Determine the differential equation that gives the amount
A(t) of salt (in pounds) in the tank at any time t before it is
emptied....

A 50-gallon tank initially contains 10 gallons of fresh water.
At t = 0, a brine solution containing 2 pounds of salt per gallon
is poured into the tank at a rate of 5 gal/min. The well-stirred
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amount of salt in the tank at the moment of overflow. Please use
differential equations to solve this problem and please put the
answer in decimal form. I did this...

A cistern contains 40 gallons of brine with 8 pounds of salt.
Another brine solution containing 2 pounds of salt per gallon is
pumped into the cistern at the rate of 4 gallons per minute and the
mixture runs out at the same rate. If the cistern is constantly
stirred, find the amount of salt in the cistern after T minutes

A tank contains 70 lb of salt dissolved in 200 gallons of water.
A brine solution is pumped into the tank at a rate of 2 gal/min; it
mixes with the solution there, and then the mixture is pumped out
at a rate of 2 gal/min. Determine A(t), the amount of salt in the
tank at time t, if the concentration of salt in the inflow is
variable and given by cin(t) = 2 + sin(t/4) lb/gal.

A tank contains 40 lb of salt dissolved in 400 gallons of water.
A brine solution is pumped into the tank at a rate of 4 gal/min; it
mixes with the solution there, and then the mixture is pumped out
at a rate of 4 gal/min. Determine A(t), the amount of salt in the
tank at time t, if the concentration of salt in the inflow is
variable and given by cin(t) = 2 + sin(t/4) lb/gal.

Using differential equation:
A 200- gallon tank initially contains 40 gallons of brine in
which 10 pounds of salt have been dissolved. Starting at t=0 ,
brine containing 5 pounds of salt per gallon flows into the tank at
rate of 6 gallons per minutes. At the same time, the well-stirred
mixture flows out of the tank at the slower rate of 4 gallons per
minute.
a)How much salt is in the tank at the end of t minutes?
b)...

A tank is filled with 10 gallons of brine in which is dissolved
5 lb of salt. Brine containing 3 lb of salt per gallon enters the
tank at a rate of 2 gal per minute, and the well-stirred mixture is
pumped out at the same rate. (a) Find the amount of salt in the
tank at any time t. (b) How much salt is in the tank after 10
minutes? (c) How much salt is in the tank after...

A tank contain 200 gallons of water. Five gallons of brine per
minute flow into the tank, each gallon of brine containing 1 pound
of salt. Five gallons of water flow out of the tank per minute.
Assume that the tank is kept well stirred. Find a differential
equation for the number of pounds of salt in the tank (call it y)
Assuming the tank intially contains no salt, solve this
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A 500-gal tank initially contains 100 gal of brine containing
75 lb of salt. Brine containing 2 lb of salt per gallon enters the
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A tank initially contains 150 gal of brine in which 60 lb of
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stirring and flows out of the tank at the rate of 5 gal/min. Let y
represent the amount of salt at time t. Complete parts a through
f.
a. At what rate (pounds per minute) does salt enter the tank
at...

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