Question

A tank contains 210 liters of fluid in which 20 grams of salt is dissolved. Brine containing 1 gram of salt per liter is then pumped into the tank at a rate of 3 L/min; the well-mixed solution is pumped out at the same rate. Find the number A(t) of grams of salt in the tank at time t.

Answer #1

A tank contains 120 liters of fluid in which 50 grams of salt is
dissolved. Brine containing 1 gram of salt per liter is then pumped
into the tank at a rate of 4 L/min; the well-mixed solution is
pumped out at the same rate. Find the number
A(t) of grams of salt in the
tank at time t.
A(t) =
__________________

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 1000 L of brine (saltwater) with 15 kg of
dissolved salt. Pure water enters the tank at a rate of 10 L/min.
The solution is kept thoroughly mixed and drains from the tank at
the same rate. How much salt is in the tank after t minutes?

A tank contains 1000 L of pure water. Brine that contains 0.05
kg of salt per liter of water enters the tank at a rate of 5 L/min.
Brine that contains 0.04 kg of salt per liter of water enters the
tank at a rate of 10 L/min. The solution is kept thoroughly mixed
and drains from the tank at a rate of 15 L/min.
(a) How much salt is in the tank after t minutes?
y=

A tank contains 1000 L of pure water. Brine that contains 0.05
kg of salt per liter of water enters the tank at a rate of 5 L/min.
Brine that contains 0.04 kg of salt per liter of water enters the
tank at a rate of 10 L/min. The solution is kept thoroughly mixed
and drains from the tank at a rate of 15 L/min.
(a) How much salt is in the tank after t minutes?
(b) How much salt...

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...

A tank contains 20 kg of salt dissolve in 5000 L of water. Brine
that contain 0.03 kg of salt per liter of water enters the tank at
a rate of 25 L/min. The solution is kept thoroughly mixed and
drains from the tank at the same rate. How much salt remains in the
tank after 13 minutes? (Keep three decimal places.)

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 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.)

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