A tank originally contains 100 gallons of fresh water. Then water containing 1/2

Question

A tank originally contains 100 gallons of fresh water. Then water containing 1/2 pound of salt per gallon is poured into the tank at a rate of 2 gallons per minute, and the mixture is allowed to leave at the same rate. After 10 minutes the process is stopped, and fresh water is poured into the tank at a rate of <<<9>>> gallons per minute, with the mixture again leaving at the same rate. Find the amount of salt in the tank at the end of an additional 10 minutes. Please give me an explantion as well. 9 gallons per min!!!

Explanation / Answer

let Q be amount of ssalt at a time t Q'(t)=2*0.5-2*Q/100 Q'(t)=1-2Q/100 integrating we get -50*ln(1-Q/50)=t from t=0 to t and Q=0 to Q 1-Q/50=e^(-t/50) Q=50*(1-e^-t/50) after t=10 min Q=9.06 gallons in the second process Q'(t)= -9Q/100 integrating we get -100/9 *lnQ =t from t=0 to 10 and Q=9.06 to Q lnQ/ln9.06 =-90/100 Q=0.1375 gallons

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