A 100 gallon tank initially contains 100 gallons of sugar water at a concentration of 0.25 pounds of sugar per gallon suppose that sugar is added to the tank at a rate of p pounds per minute that sugar water is removed at a rate of 1 gallon per minute and that water in the tank is kept well mixed. What value of P should we pick so that that when 5 gallons of sugar solution is left in the tank the concentration is .5lbs of sugar/gallon?

At the start, the tank contains

(0.25 lb/gal) * (100 gal) = 25 lb

of sugar. Let be the amount of sugar in the tank at time . Then .

Sugar is added to the tank at a rate of P lb/min, and removed at a rate of

and so the amount of sugar in the tank changes at a net rate according to the separable differential equation,

Separate variables, integrate, and solve for S.

Use the initial value to solve for C :

The solution is being drained at a constant rate of 1 gal/min; there will be 5 gal of solution remaining after time

has passed. At this time, we want the tank to contain

(0.5 lb/gal) * (5 gal) = 2.5 lb

of sugar, so we pick P such that

26 is 33.33% of 78

step-by-step explanation:

26 is what percent of 78?

26 is p% of 78

equation: y = p% * x

solving our equation for p

p% = y/x

p% = 26/78

p = 0.3333

convert decimal to percent:

p% = 0.3333 * 100 = 33.33%