Traffic on a three$-$lane $($in each direction$)$ freeway observes the following Greenshields flow relationship:

$V=60D(1-\frac{D}{360})$

where $V$ is the traffic volume on vehicle per hour, and $D$ is the traffic density in vehicles per mile. At $10$:$00$ am$,$ an accident occurs at point $A($in the following

Figure$).$ The vehicles involved immediately pull off onto the shoulder of the roadway, but traffic passing the incident slows to $10$ mph as drivers survey the

damage on the side of the road $($sometimes called "spectator slowing"$).$ Lucy enters the freeway via the ramp at point B$,$ also at $10$:$00$ am$.$ Upon entering the

freeway, she notes that traffic on the freeway is moving along at about $40$ mph $.$

A$.$ How fast $($i$.$e$.,$ at what speed$)$ will back up from the "spectator slowing" progress upstream of the accident site?

answer as a positive numerical number only in units of miles per hour and rounded to the nearest whole number, i$.$e$.$ XX$.)$

B$.$ When $($i$.$e$.,$ at what time$)$ will Lucy first hit slowing traffic due to the accident?