ank A contains 80 gallons of water in which 20 pounds of salt has been dissolved. Tank B contains30 gallons of water in which 5 pounds of salt has been dissolved. A brine mixture with a concentrationof 0.5 pounds of salt per gallon of water is pumped into tank A at the rate of 4 gallons per minute. The well-mixed solution is then pumped from tank A to tank B at the rate of 6 gallons per minute. The solution from tank B is also pumped through another pipe into tank A at the rate of 2 gallonsper minute, and the solution from tank B is also pumped out of the system at the rate of 4 gallons perminute. Find the differential equations with initial conditions for the amounts, x(t)andy(t), of saltin tanks A and B, respectively, at time t.

x(0)=20,y(0)=5

Step-by-step explanation:

We are given that

Tank A contains water=80 gallons

x(0)=20,y(0)=5

Tank B contains water=30 gallons

Rate=4 gallon/min

Concentration of salt  is pumped into tank=0.5 pound /gallon of water

Solution pumped from tank A to tank B at the rate=6 gallons/min

Solution pumped from tank B to tank A at the rate=2gallon/min

Solution from tank B is pumped out of the system at the rate=4 gallon/min

We have to find the DE at time t

For x

Rate in=

Rate in=

Rate out=

Rate out=3x/40[/tex]

Rate in-Rate out

For y

Rate in=

Rate in=3/40x

Rate out=

Rate out=y/5

Rate in-Rate out

10010010001010010101001001010010100101010010101010010010101010110010001011010010010001

step-by-step explanation:

10.416 m/s

step-by-step explantion:

distance=100m

time= 9.6s

average speed=100/9.6

=10.416 m/s