A 50 L tank initailly contains 10 L of fresh water, At t=0, a brine solution containing 1 lb of salt per gallon is poured into the tank at the rate of 4 L/min, while the well-stirred mixture leaves the tank at the rate of 2 L/min. Then the amount of time required for overflow to occur in

Options

A. 20 lb
B. 50 lb
C. 30 lb
D. None of these

Answer

D

Explanation

`(dQ)/(dt)+2/(10+2t)Q=4`
This is a linear equation, It solution is `Q=(40t+4t^(2)+c)/(10+2t)`……….(1)
At `t=0, Q=a=0`. Substituting these values into equation (1), we find that c=0. We require Q at the moment of overflow which from part (a) is t=20. Thus,
`Q=(40(20)+4(20)^(2))/(10+2(20))=40 lb`