Answer
$[4, \frac{39}{4}]\ sec$ or from (and inclusive) 4 to 9.75 sec.
Work Step by Step
Step 1. Given $s=-16t^2+220t$, let $s\ge624$, we have $-16t^2+220t\ge624$
Step 2. Rewrite the inequality as $16t^2-220t+624\le0$ or $(4t-16)(4t-39)\le0$
Step 3. Identify the boundary points as $t=4, \frac{39}{4}$
Step 4. Use test points at $t=0, 5, 10$ 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 $[4, \frac{39}{4}]\ sec$ that is from (and inclusive) 4 to 9.75 sec.
