Question

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

Answer #1

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well-stirred mixture is withdrawn from the tank at a rate of 5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?

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 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.

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...

Consider a 2500-gallon capacity tank of water that contains 100
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 5 gallons per minute. (a) Set up and
solve the initial value problem to find the amount of salt in the
tank as a function of time....

A 24 gallon tank is filled with pure water. Water which has a
concentration of 6g of salt per gallon flows into the tank at a
rate of 2 gallons/min, and the mixture is stirred to a uniform
concentration. Water also leaks from the tank at the same rate, 2
gallons/min.
Find a differential equation describing the rate of change of salt
in the tank.
Hint: The concentration of salt in the tank is
S(t)/24, where
S(t) is the total...

A 50-gallon tank initially contains 10 gallons of fresh water.
At t = 0, a brine solution containing 2 pounds of salt per gallon
is poured into the tank at a rate of 5 gal/min. The well-stirred
mixture drains from the tank at a rate of 3 gal/min. Find the
amount of salt in the tank at the moment of overflow. Please use
differential equations to solve this problem and please put the
answer in decimal form. I did this...

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.

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 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?

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 6 minutes ago

asked 10 minutes ago

asked 16 minutes ago

asked 42 minutes ago

asked 54 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago