Question

A tank with capacity of 600 gal of water originally contains 200 gal of water with 100 lb of salt in solution. Water containing 1 lb of salt per gallon is entering at a rate of 3 gal/min, and the mixture is allowed to flow out of the tank at a rate of 2 gal/min. Let Qct) Ib be the amount of salt in the tank, Vt) gal be the volume of water in the tank. Find the amount of salt in the tank at any time prior to the instant when the solution begins to overflow. 31° + 1200 + 40000 Q(t)- 2(t+200) 833.33 Find the concentration (in pounds per gallon) of salt in the tank when it is on the point of overflowing. (Round your answer to three decimal places.) X lb/gal Find the theoretical limiting concentration if the tank had infinite capacity. 3 X lb/gal H GO Tutorial 2

Answer 1

Ang Assume that the amount of salt in the tank at time t is Q. then, sake of change of salt in tank is any de dt dQ dt rin-hout 1 lb/gal x 3 gall mio 3 lb/min. initially there are 200 gulo of ander in the took cohich is increasing at the rate of I gal/min. So the tank capacity will get filled in 300 minutes. Quantity of water in the tank at any time t=(2004+) gal So, the rate out YQ(t) lb/min 200++ = 2Q 200+t da = 3- 2Q #200 + 2 ++200 Q = 3 now lb/min (n=2) da de inlegsrating factoon is = e 261(44200) In (t+200)? = (t+200) :: Q (H20072 - 5 3 (t+200) 2.4 + (+-+200) + c :: Q = (t+200)+ t+2002 initially when t=0 Q = 100 lb e

100 = 200 + с. (20012 G= -100(200)2 4000000 Q= +4200 - 4000000 9ь (t+2009 when Cohen t= 300, Q=500 4000000 (5002 = 484 db so 484 600 150 Q/gal 121 lbigel. colen tank has infinite capacity the concertzation of Salt in the tank will increase at the rate of llblgal, Since the initial quality of salt will have decimal infinite quality of water. effect On Thank you.