Question

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

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 3 gal/min,with the mixture again leaving at
the same rate. Find the amount of salt in the tank at the...

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 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

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 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 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 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 tank contains 300-gallon of pure water. At time t = 0, a
solution containing 2 lb of salt per gallon flows into the tank at
a rate of 1 gallon per minute, and the well-stirred mixture flows
out at a rate of 2 gallons per minute. Find the amount(in lb) of
salt Q in the solution as a function of t in minutes.
please show work and explain thank you

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.

A tank contains 144 gal of water and 48 oz of salt. Water
containing a salt concentration of (1/6+1/12sin t) oz/gal flows
into the tank at a rate of 3 gal/min, and the mixture in the tank
flows out at the same rate.
(a) Find the amount of salt in the tank at any time.
The amount of salt in the tank is Q(t)=

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