Question

7 APPLICATIONS OF IST ORDER DE: Problem 10 Previous A b , List Next (1 pt) A tank contains 90 kg of salt and 1000 L of water. Pure water enters a tank at the rate 12 L/min. The solution is mixed and drains from the tank at the rate 6 L/min. (a) What is the amount of salt in the tank initially? amount = (kg) (b) Find the amount of salt in the tank after 2 hours. amount = (kg) (c) Find the concentration of salt in the solution in the tank as time approaches infinity. (Assume your tank is large enough to hold all the solution.) concentration = (kg/L) Note: You can earn partial credit on this problem. Preview Answers Submit answers You have attempted this problem 1 time. Your overall recorded score is 67%. You have 4 attempts remaining. Page generated at 02/05/2020 at 02:27pm PST WebWork O 1996-2011 The WebWork Project

Answer 1

rom the given information, the tank in 6 contained 90 kg of salt. o amount = 190 kg The tank initially contains 90 kg of salt, Initial condition is 8(0) =90. 8(t)= The amoun The tank the amount of salt in the tank at timet. 90 kg of salt, hence, the o da = rare in - rate out dt A pure water, hence rate inise Pure water enters a tank at There is no salt in pure water, hence & . (0kg/L) (12L/min) =0 legl mein The solution drains from the tank at a rate of 64 min We do not know the amount of salt in the tank (this is dit). Mas the amount of water in the tank is also - Changing with respect to time water is coming in e at 12 Linun and a solution is leaving 6 Limin, hence After every minute we have oL extra of liquid in the tank. The amount of liquid at time t is then 1000+ st. Thus the rate going out is (100076t) (6 ) = 8 Guvern 1000 fot 1000 tot 3060)=90 - enlarin lood+6+1+Ç enial =-en 11000+ 6+1+1° Q=CC1000+6757

SC = 90000 t=0, 8=90 Q10) = _ 90 C=900 8(t) =/90000 1000+6+/ 2 hour = 2x60 min = 120 minutes of salt in the tank after 2 hours = Q(120) AL120) = 90000 9000 =12250kg 1000+ izox6 = 172 173 17 The amount of salt in the 0 lim act) = lim (90000 =0 tyo t30 C1ooo+6) Thus No more salt left in the tank amount of time. concentration of salt = 10 kg IL after infinite