Question

A tank with a capacity of 400 gallons originally contains 100 gallons of water with 25 pounds of salt in solution. Water containing 1/2 pound of salt per gallon is entering at a rate of 4 gallons per minute, and the mixture is allowed to flow out of the tank at a rate of 1 gallon per minute. FIND the amount of salt in the tank at any time prior to the instant when the solution begins to overflow.

Answer 1

Solutions given data : v(t) = 400 gal Vola 100 gal. Q(0) 2 25 Tb tank at time tis v (t) = 100+t da .: Sate in - Xate out : dt Here I Rate in a 1x4 = 4 QIZ) Rate out= 1x Q4). (t) 100 Hz) Thus, da : 4- Qlt) . ,Q (0) - 25 dt 100+t de + Q (t) H dt loott Integration factor IF = e note dt In (100 +t) = (100+ 1

differential The solution of fine art equation as, Q (t) (100++)?: Su(100++* dt S M 900*23 +C • 6100++)? + Q (t) = (100+t) + 100+t) ? Here, c is an arbitrary constant : to find the constanta use the initial condition Q(0)= 95 26073 6100+0] + "160 705 ? 2650 - 100 + termo occo = -75 C=-750000 - 75 oooo - thes, Q(t) = (1004t) - Noott)? Therefore, the amount of salt in the tank at any time it is. 1964) = (100+t) - 7600