A 500 gallon tank originally contains 100 gallons of fresh water. Beginning at time t=0, water containing 50 percent pollutants flows into the tank at the rate of 2 gal/min and the well stirred solution leaves at the rate of 1 gal/min. Find the concentration of pollutants in the tank at the moment it overflows. The answer is 48% my attempt, something is wrong as i did not get that answer or anywhere near it. rate in: 2 x 0.50 rate out: 1 x s(t)/(100+t) s'(t) = 1- s(t)/(100+t) s'(t) + s(t)/(100+t) = 1 a(t) = 1/(100+t) , b(t) = 1 using u(t) = exp(integ(a(t)dt)): u(t) = exp(integ(a(t)dt)) u(t) = exp (ln (100+t)) u(t) = 100+t using d/dt u(t)s(t) = u(t)b(t): d/dt [(100+t)s(t)]= (100+t)(1) (100+t)s(t)=integ(100+t) (100+t)s(t) = 100t + 1/2t^2 + C s(t) = [100t + 1/2t^2 +C ]/(100+t) sub s(0) = 0 into s(t) [is this even correct?] 0 = [0+0+c]/[100+0] c= 0 s(t) = [100t + 1/2t^2]/(100+t) c(t) = s(t)/100 c(t) = [100t + 1/2t^2]/100(100+t) then i found when the tank overflow: 500 = 100+t t= 400 then found c(t) c(400) = [100(400)+1/2(400)^2]/100(100+400) c(400) = 2.4 which is wrong. can anyone help me?