A shop is open $9$ AM $-7$ PM$.$ The function $r(t),$ graphed above, gives the rate at which customers arrive $($in people$/$hour$)$ at time $t,$ where $t$ measures time in hours since $9$ AM$.$ Suppose that the salespeople can serve customers at a rate of $75$ people per hour. Answer the following questions:

A$.$ At what time will people begin having to wait in line before getting served $($because the volume of people arriving has become too great$)?$

Answer: hours after opening.

B$.$ When is the line longest? Answer: $$ hours after opening.

C$.$ How many people are in the line at the time when it's the longest?

Answer: $$ people.

D$.$ When does the line vanish?

Answer: $$ hours after opening.