A large mixing tank currently contains 350 gallons of water, into which 10 pounds of sugar have been mixed. A tap will open, pouring 20 gallons of water per minute into the tank at the same time sugar is poured into the tank at a rate of 3 pounds per minute. Find the concentraion (pounds per gallon) of sugar in the tank after 15 minutes. Is that a greater concentration than at the beginning?

AnswerLet t be number of minutes since tap is openedwater is increased by 20 gallons of water per minute.sugar increase rate of 3 pounds per minutewater :- W(t) = 350 + 10 tsugar :- S(t) = 10 + 3 tconcentrationC(t) = [tex]\dfrac{S(t)}{W(t)}[/tex]at t = 15 minutesC(15) = [tex]\dfrac{S(15)}{W(15)}[/tex]C(15) = [tex]\dfrac{10 + 3\times 15 }{350 + 10\times 15}[/tex]C(15) = 0.11at beginning t = 0 minutesC(0) = [tex]\dfrac{S(0)}{W(0)}[/tex]C(0) = [tex]\dfrac{10 + 3\times 0}{350 + 10\times 0}[/tex]C(0) = 0.0286C(15) > C(0)hence, concentration is increasing as time is passing.