Suppose that a cascade of two tanks has two tanks of equal$$ volume, where liquid flows into tank$1,$ then from tank $1$ to tank$2,$ and then out of tank $2.$ Tank $1$ initially contains $80$ gal of pure ethanol and tank $2$ initially contains $80$ gal of pure water. Pure water flows into tank $1$ at $8$gal$/$min$,$ and the other two flow rates are also $8$gal$/$min$.($a$)$ Find the amounts$$ x$($t$)$ and$$ y$($t$)$ of ethanol in the two tanks at time t greater than over equal $0.($b$)$ Find the maximum amount of ethanol ever in tank $2.$