The driver in problem $2$ stops at an intersection with a two$-$way stop sign. Assume that the width of the intersection in $24$ ft and the car is $20$ ft long. If the driver's perception$-$reaction time is $0\mathrm{.}75$ seconds, determine if he can clear the intersection safely for the following conditions?

$($a$)$ When the through traffic is quite heavy and the average gap between vehicles is $5$ seconds.

$($b$)$ If the average gap between vehicles increases to $10$ seconds.