Question

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 long time?

Answer #1

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 large tank is filled with 80 gallons of fluid in
which 2 pounds of salt are dissolved. Brine containing 1/2 pound of
salt per gallon is pumped into the tank at a rate of 3 gal/min. The
well-mixed solution is then pumped out at the same rate of 3
gal/min. Find the concentration of salt in the tank after 30
minutes.

A large tank contains 800 gal of water in which 42 lb of salt
are dissolved. Brine
containing 2 lb of of dissolved salt per gal is pumped into the
tank at a rate of
4 gal per minute, and the mixture, kept uniform by stirring, is
pumped out at
the same rate.
(a) Find the amount x(t) of salt in the tank, at time t.
(b) How long will it take for the amount of salt in the tank...

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.

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 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.

A 110 gallon tank initially contains 5 lbs salt dissolved in 60
gallons of water. Brine containing 1 lb salt per gallon begins to
flow into the tank at the rate of 3 gal/min and the well-mixed
solution is drawn off at the rate of 1 gal/min. How much salt is in
the tank when it is about to overflow? (Round your answer to the
nearest integer.)

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
tank at a rate of 5 gal/s, and the well-mixed brine in the tank
flows out at the rate of 3 gal/s. How much salt will the tank
contain when it is full of brine?

A 100 gallon tank is filled with brine solution containing 50
pounds of salt. Pure water enters the tank a rate of 10 gal per
hour. Well mixed solution leaves the first tank at the same rate
(10 gal/hr) and enters a second 100 gallon tank initially
containing 10 pounds of salt. How much salt is in tank 2 at any
time?

A tank initially contains 150 gal of brine in which 60 lb of
salt are dissolved. A brine containing 4 lb/gal of salt runs into
the tank at the rate of 6 gal/min. The mixture is kept uniform by
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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