Question

- Anthony works at a plant that makes a solution for brining hotdogs. A tank with a capacity of 2000 liters originally contains 1500 liters of fresh distilled water. Two pipes pour different mixtures of brine into the tank. The big pipe pours 1 kg of salt per minute at a rate of 6 liters per minute. The smaller pipe pours a mixture containing 2 kg of salt per minute at a rate of 4 liters per minute. Assume the salt and water are well mixed.

- If the mixture flows out of two pipes at a rate of 5 liters per minute each, what is the amount of salt in the tank at any time . What is the amount of salt at 10 minutes? Does solution reach a steady state of salt and if so, what is it? Graph the solution.

- Anthony accidentally shuts off one of the outflow pipes and doesn’t notice. When will the tank overflow and how much salt will it contain? Graph the solution.

- He notices that the tank is overflowing and turns off the big pipe. How long will it take for the tank to return back to 1500 liters of the mixture. What will happen in the long run? Graph the solution.

Answer #1

A tank originally contains 130 liters of water with 10 grams of
salt in solution. Beginning at t=0, water containing 0.1 grams of
salt per liter flows into the tank at a rate of 2 liters per minute
and the uniform mixture drains from the tank at a rate of 2 liters
per minute. Letting t be time in minutes and Q be the amount of
salt in the tank at time t measured in grams, formulate an initial
value...

A tank originally contains 120 liters of water with 5 grams of
salt in solution. Beginning at t=0, water containing 0.4 grams of
salt per liter flows into the tank at a rate of 2 liters per minute
and the uniform mixture drains from the tank at a rate of 2 liters
per minute. Letting t be time in minutes and Q be the amount of
salt in the tank at time t measured in grams, formulate an initial
value...

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?

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 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 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 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

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