Answer
$[6, \frac{31}{4}]\ sec$ or from (and inclusive) 6 to 7.75 sec.
Work Step by Step
Step 1. Given $s=-16t^2+220t$, let $s\ge744$, we have $-16t^2+220t\ge744$
Step 2. Rewrite the inequality as $16t^2-220t+744\le0$ or $(4t-24)(4t-31)\le0$
Step 3. Identify the boundary points as $t=6, \frac{31}{4}$
Step 4. Use test points at $t=0, 7, 8$ for the signs of the left side expression and get $+, -, +$ for the three regions.
Step 5. The solution requires negative (middle region), thus the time interval is $[6, \frac{31}{4}]\ sec$ that is from (and inclusive) 6 to 7.75 sec.
