Question

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 salt solution remain.

Answer #1

A tank originally contains 100 gal of fresh water. Then water
containing 1/2 lb of salt per gallon is poured into the tank at a
rate of 2 gal/min, and the mixture is allowed to leave at the same
rate. After 10 min the process is stopped, and fresh water is
poured into the tank at a rate of 5 gal/min, with the mixture again
leaving at the same rate. Find the amount of salt in the tank at
the...

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 tank originally contains 100 gal of fresh water. Then water
containing
1
2
lb of salt per gallon is poured into the tank at a rate of 2
gal/min, and the mixture is allowed to leave at the same rate.
After 10 min the process is stopped, and fresh water is poured into
the tank at a rate of 3 gal/min,with the mixture again leaving at
the same rate. Find the amount of salt in the tank at the...

A 100-gallon tank initially contains pure water. A solution of
dye containing 0.3 lb/gal flows into the tank at the rate of 5
gal/min and the resulting mixture flows out at the same rate. After
15 min, the process is stopped and fresh water flows into the tank
at the same rate. Find the concentration of dye in the tank at the
end of 30 min. Ans.: 0.075 lb/gal

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 gallons of pure water. A salt solution with
concentration 2.5 lb/gal enters the tank at a rate of 4 gal/min.
Solution drains from the tank at a rate of 4 gal/min. Find the
eventual concentration of the salt solution using a qualitative
analysis rather than by actually solving the DE.

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 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...

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 holds 100 gal of brine solution. At t = 0,
fresh water is poured into the tank at the rate of 5 gal/min, while
the well-stirred mixture leaves the tank at the same rate. After 20
min, the tank contains 20/e lb of salt. Find the initial
concentration of the brine solution inside the tank. Ans.: 0.20
lb/gal

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