Question

13. A 600 gallon capacity tank initially contains 50 pounds of salt dissolved in 100 gallons of water. Water containing 2 pounds of salt per gallon enters the tank at a rate of 6 gallons per minute (assume the salt is evenly distributed throughout the water in the tank). Water is drained from the tank at a rate 4 gallons per minute. How many pounds (rounded to 1 decimal place) of salt will be in the tank when the tank is full?

Answer 1

Let y represent the emocent of salt in the tank at time t, where t is given in minutes. and Then yo 50 at tzo en de la ante in a rate out dt dy 6 gallon - 2 porend -X gallon 4x4 gallon, 100 gallon mini min dt dy y poconds/men 12 porcends /men min 25 at 12 + ♡ dy at 25 multeply the with. both sides abore equation on 8425 1/25 1/25 e 널25 4.3 12-е dy TE е + 25 165 j 425 y= 12e dt 425 thos ang tc tas = (25X12) e 300 4256 e g

t/5 Je 300 + C'e Now, ap applying Pnitial Conditions toe y=50 at t=0 50= 300 t otcle) - 250 CE 50 300 + C = -t/25 - 250 e So, y= 300 Now, we need to find at what time the tank is full (600 gallons). Philially the tank with loo solution gallons of aso, 600 gallons 100 + (6-4) Gallery x timing min 500 = at :, t=250 minutes, It will take 250 minetas to full the tank Now the quantity of selt (in pocends) present in the tank when it Pp fall is given by 7 €=250)= 300-250 (6) y eso) = 300-25066') =-299.98 poundle Ans: 299.98 pounds