Question

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 to
become 60 lb?

Answer #1

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 100 gal of brine made by dissolving 80 lb of
salt in water. Pure water
runs into the tank at the rate of 4 gal/min, and the mixture,
kept uniform by stirring runs
out at the same rate. Find the amount of salt in the tank at
t=8 min.

Suppose the tank in the figure below initially contains 800 gals
of water in which 190 lbs of salt is dissolved. Brine runs in at a
rate of 10 gal min and each gallon contains .5 lb of dissolved
salt. The mixture in the tank is kept uniform by stirring. The
brine solution is withdrawn from the tank at a rate of 8 gals min.
Let s(t) represent the amount of salt in the tank at anytime t, and
develop...

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 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 initially contains 100 pounds of salt dissolved in 500
gallons of water. Saltwater
containing 5 pounds of salt per gallon enters the tank at the
rate of 2 gallons per minute.
The mixture (kept uniform by stirring) is removed at the same
rate of 2 gallons per minute.
How many pounds of salt are in the tank after an hour?

A tank initially contains 100 gal of a salt-water solution
containing 0.05 lb of salt for each gallon of water. At time zero,
pure water is poured into the tank at a rate of 2 gal per minute.
Simultaneously, a drain is opened at the bottom of the tank that
allows the salt-water solution to leave the tank at a rate of 3 gal
per minute. What will be the salt content in the tank when
precisely 50 gal of...

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 300-gal capacity tank contains a solution of 200 gal of water
and 50 lb of salt. A solution containing 3 lb of salt per gal is
allowed to flow into the tank at the rate of 4 gal/min. The mixture
flows from the tank at the rate of 2 gal/min. How many pounds of
salt are in the tank at the end of 30 min? When does the tank start
to overflow? How much salt is in the tank...

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