A high$-$rise building with $25$ floors $($the ground floor to the $24$th floor$)$ is in fire, and people need to evacuate from the building immediately. The recognition time for all people ranges from $20$ to $40$ s$,$ the response time ranges from $40$ to $90$ s$.$ The maximum$/$minimum distance from each floor to its staircases is $100$ m$/5$ m$,$ and walking speed ranges from $1\mathrm{.}0$ to $1\mathrm{.}5$ m$/$s$.$

$($a$)$ Suppose each occupant needs $20$ s from one floor to the lower floor downstairs, what is the total time of the evacuation?

$($b$)$ The visibility is large than $20$ m before $300$ s of the fire ignition on the ground floor near the entrance. When the time exceeds $300$ s$,$ the visibility could be simplified as the equation:

Visibility $=7500/$time

Discuss whether all people can evacuate successfully based on current information and explain why.