Answer
$4:00~p.m.$.
Work Step by Step
$$L=-0.270t^2+3.59t+83.1$$
Substituting $L=93$ into the equation:
$$93=-0.270t^2+3.59t+83.1$$
$$9300=-27t^2+359t+8310$$
$$-27t^2+359t-990=0$$
Using the quadratic formula:
$$t=\frac{-359\pm\sqrt{359^2-4(-27)(-990)}}{2(-27)}=\frac{-359\pm\sqrt{21961}}{-54}$$
$$t_1=\frac{-359+\sqrt{21961}}{-54}=3.90$$
$$t_2=\frac{-359-\sqrt{21961}}{-54}=9.39$$
With the constraint $2\leq t\leq7$, take $t=3.9\approx4$.
Then, the time is:
$$time=0+4=4:00~p.m.$$
