Answer
(a) $1\ sec$ and $5\ sec$
(b) $6\ sec$.
Work Step by Step
(a) Given the model equation $s = -16t^2 + 96t$, let $s=80$, we have $-16t^2 + 96t=80\longrightarrow t^2-6t+5=0\longrightarrow (t-1)(t-5)=0$, thus $t=1\ sec$ and $t=5\ sec$
(b) When it returns to the ground, $s=0$, we have $-16t^2 + 96t=0$ which gives $t=0$ and $t=6\ sec$. Discard $t=0$ as it is the starting point, thus we have $t=6\ sec$.