Question

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?

Answer #1

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.

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 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.)

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 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?

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...

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...

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...

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 tank contain 200 gallons of water. Five gallons of brine per
minute flow into the tank, each gallon of brine containing 1 pound
of salt. Five gallons of water flow out of the tank per minute.
Assume that the tank is kept well stirred. Find a differential
equation for the number of pounds of salt in the tank (call it y)
Assuming the tank intially contains no salt, solve this
differential equation. At what time will there be 100...

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