Question

A 200 gallon tank initially has 100 gallons of a salt solution that contains 5 lbs of salt. A salt solution is pumped into the tank at a rate of 4 gallons per minute with a concentration of 1 lb of salt per gallon. The well-mixed solution is pumped out of the tank at a rate of 2 gallons per minute. How much salt will be in the tank after 30 minutes? Round to one decimal place.

Answer #1

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 2000 gallon tank initially contains a mixture of 750 gallons
of water and 100 gallons of salt. Water is added at a rate of 8
gallons per minute, and salt is added at a rate of 2 gallons per
minute. At the same time, a well mixed solution of "brine" is
exiting at a rate of 5 gallons per minute. What percentage of the
mixture is salt when the tank is full?

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 200-gallon tank is currently half full of water that contains
30 pounds of salt. A solution containing 3 pounds of salt per
gallon enters the tank at a rate of 5 gallons per minute, and the
well-stirred mixture is withdrawn from the tank at a rate of 5
gallons per minute. How many pounds of salt are in the tank 10
minutes later?

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 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.

3. A tank initially contains a solution of 10 lbs of salt
dissolved in 60 gallons of water. At time t(0) = 0, water that
contains 1/2 lb of salt per gallon is added tot he tank at a rate
of 6 gal/min, and the resulting solution leaves the tank at the
same rate. (Trench: Sec 4.3, 9)
(a) What is the initial condition for the IVP?
(b) Write a diď¬€erential equation to describe the rate of change
dQ/dt in...

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.

initially, a large tank with a capacity of 250 gallons contains 125 gallons of clean water. A saline solution with a concentration of 4 pounds per gallon flows into the tank at a rate of 20 gallons per minute. the solution mixes perfectly well while drawing at a rate of 10 gallons per minute. Find: 1) the amount of salt in the tank at the time it fills up (in pounds) 2) the rate at which the salt comes out...

Consider a 400-gallon capacity tank of water that contains 200
gallons of water in which 10 pounds of salt are dissolved. Suppose
that water with a salt concentration of 2 pounds per gallon enters
the tank at a rate of 6 gallons per minute, is well-stirred, and
the mixture leaves the tank at 9 gallons per minute.
Set up and solve the initial value problem to get the amount of
salt as a function of time.
Use this function to...

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