Problem $1$: $(10$ points$)$

Two full $42-$gallon tanks begin draining water at $t=0$ minutes. Tank Alpha's volume is changing at a constant rate of $-4$gal$/$min$.$ The rate at which Tank Bravo's volume is changing is given by $r(t)=\frac{1}{2}{t}^2-3t-4$ gal$/$min$.$

$($a$)[4$ points$]$ In the picture below, what is the physical interpretation of the shaded region $0t6?$

$($b$)[6$ points$]$ Which tank drains first?