Question

Consider two brine tanks connected as shown in the figure. Pure water flows into the top of tank 1 at a rate of 5 L/min. The brine solution is pumped from tank 1 into tank 2 at a rate of 25 L/min, and from tank 2 into tank 1 at a rate of 20 L/min. A brine solution flows out the bottom of tank 2 at a rate of 5 L/min. Suppose there are 60 L of brine in tank 1 and 140 L of brine in tank 2. Let x be the amount of salt, in kilograms, in tank 1 after t minutes, and y the amount of salt, in kilograms, in tank 2 after t minutes. Assume that each tank is mixed perfectly. Set up a system of first-order differential equations that models this situation. [ x' y' ] = [ [ ] [ ] [ ] [ ] ] [ x y ]

          Consider two brine tanks connected as shown in the figure. Pure water flows into the top of tank 1 at a rate of 5 L/min. The brine solution is pumped from tank 1 into tank 2 at a rate of 25 L/min, and from tank 2 into tank 1 at a rate of 20 L/min. A brine solution flows out the bottom of tank 2 at a rate of 5 L/min. Suppose there are 60 L of brine in tank 1 and 140 L of brine in tank 2. Let x be the amount of salt, in kilograms, in tank 1 after t minutes, and y the amount of salt, in kilograms, in tank 2 after t minutes. Assume that each tank is mixed perfectly.

Set up a system of first-order differential equations that models this situation.

[ x' y' ] = [ [ ] [ ] [ ] [ ] ] [ x y ]

Consider two brine tanks connected as shown in the figure. Pure water flows into the top of tank 1 at a rate of 5 L/min. The brine solution is pumped from tank 1 into tank 2 at a rate of 25 L/min, and from tank 2 into tank 1 at a rate of 20 L/min. A brine solution flows out the bottom of tank 2 at a rate of 5 L/min. Suppose there are 60 L of brine in tank 1 and 140 L of brine in tank 2. Let x be the amount of salt, in kilograms, in tank 1 after t minutes, and y the amount of salt, in kilograms, in tank 2 after t minutes. Assume that each tank is mixed perfectly.

Set up a system of first-order differential equations that models this situation.

[ x' y' ] = [ [ ] [ ] [ ] [ ] ] [ x y ]

Added by Robert G.

Question

Please give Ace some feedback