Question

A tank initially contains 150 gal of brine in which 60 lb of salt are dissolved. A brine containing 4 lb/gal of salt runs into the tank at the rate of 6 gal/min. The mixture is kept uniform by stirring and flows out of the tank at the rate of 5 gal/min. Let y represent the amount of salt at time t. Complete parts a through f.

a. At what rate (pounds per minute) does salt enter the tank at time t?

b. What is the volume of brine in the tank at time t?

c. At what rate (pounds per minute) does salt leave the tank at time t?

d. Write down and solve the initial value problem describing the mixing process.

e. What is the solution to the initial value problem?

f. Find the concentration of salt in the tank 27 min after the process starts.

Thank you in advance. Please show your work and explain.

Answer #1

A large tank contains 800 gal of water in which 42 lb of salt
are dissolved. Brine
containing 2 lb of of dissolved salt per gal is pumped into the
tank at a rate of
4 gal per minute, and the mixture, kept uniform by stirring, is
pumped out at
the same rate.
(a) Find the amount x(t) of salt in the tank, at time t.
(b) How long will it take for the amount of salt in the tank...

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