Suppose that a large mixing tank initially holds 400 gallons of water in which 65 pounds...

Suppose that a large mixing tank initially holds 400 gallons of water in which 65 pounds of salt have been dissolved. Another brine solution is pumped into the tank at a rate of 6 gal/min, and when the solution is well stirred, it is pumped out at a slower rate of 5 gal/min. If the concentration of the solution entering is 3 lb/gal, find the amount of salt in the tank after 10 minutes.

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Fuom ,2) and (3 dy dt in-yout 1 dy 18 (S dt dy + S4 18 dt whis is inear ditteruntial equation dt Snl400tt) 5 Ame nfietre If e : e 5Lne 5 (ttho5 Ct+400) auy Ctt400) + 18 Ct4400)5 dt 4 dy Ctt400)+ (t+40) 5y 18 t+4o0) 7 dt dt at 18 Ctt400) c'. 6

3Ct 4o0)C Snitially theru uas 65 pounas of Salt dissolmed YCo) 65. 66 LOR4 -S 3 Ct+4o0) + C[t+400 4Co)=65 -5 65= 3(400) + c [400 65=1200 + C 5 (4o) F C -454Ox 1o -1135 (400)5 CE -454 x10" yctt4oo3Ct+ 4o 454x 10" After Lo munty CIo) 0410 0 30410-454x 1o") 30410) - 454 x 10 (41) 5 105 12 30- 3.918 X10x 10 -1230-3.918 226 082 pounds of salt

Colby Messinger answered 2 years ago

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