(a) 15 people per hr
(b). let the rate that people enter be
$r=220te^{-0.4t}+15$
use the product rule to determine the derivative of the rate, and set equal to zero to determine critical value(s) of $t$ ...
$r'(t)=220e^{-0.4t}(-0.4t +1) = 0 \implies t=2.5$
So, how would you justify $r(2.5)$ is a maximum?
well, it showed back up ...
The problem gave a rate that people enter a festival as
$\dfrac{dE}{dt}=220te^{-0.4t}+15$, $0 \le t \le 12$, where $t=0$ is noon.
part (a) asked for the rate of entrance at $t = 0$
part (b) asked for the time when the rate of entrance is a maximum.