Question

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?

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well-stirred mixture is withdrawn from the tank at a rate of 5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

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?

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 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...

A 100 gallon tank is filled with brine solution containing 50
pounds of salt. Pure water enters the tank a rate of 10 gal per
hour. Well mixed solution leaves the first tank at the same rate
(10 gal/hr) and enters a second 100 gallon tank initially
containing 10 pounds of salt. How much salt is in tank 2 at any
time?

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 500-gallon tank initially contains 100gal of brine containing
50lb of salt. Brine containing 2lb of salt per gallon enters the
tank at the rate of 4gal per minute and the well stirred solution
leaves the tank at a rate of 8gal per minute.
(a) How long will it be before the tank is empty
(b) Determine the differential equation that gives the amount
A(t) of salt (in pounds) in the tank at any time t before it is
emptied....

A tank initially contains 100 gal of a salt-water solution
containing 0.05 lb of salt for each gallon of water. At time zero,
pure water is poured into the tank at a rate of 2 gal per minute.
Simultaneously, a drain is opened at the bottom of the tank that
allows the salt-water solution to leave the tank at a rate of 3 gal
per minute. What will be the salt content in the tank when
precisely 50 gal of...

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.)

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)...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 33 minutes ago

asked 44 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

asked 2 hours ago

asked 2 hours ago

asked 3 hours ago