Problem $2$Consider an $8-$car caravan, where the propagation speed is $100$ km$/$hour$,$ each car takes $1$ minute to pass a toll both. The caravan starts in front of toll booth A$,$ goes through toll booth B$,$ and ends after passing toll booth C$.$ Let dAB and dBC be the distance between A$-$B$,$ and B$-$C$.$ a$)$Suppose dAB $=$ dBC $=10$ km$.$ What is the end$-$to$-$end delay if the caravan travels together $($i$.$e$.,$ the first car must wait for the last car after passing each toll booth$)?$b$)$Repeat a$),$ but assume the cars travel separately $($i$.$e$.,$ not waiting for each other$).$ c$)$Repeat a$)$ and b$),$ but suppose dAB $=$ dBC $=100$ km$.$ d$)$Still suppose dAB $=$ dBC $=100$ km$.$ Suppose toll booth B takes $10$ minute to pass each car $($A and C still takes $1$ minute per car$).$ Where is the first car when the second car passes B$?$ e$)$Under the assumption of d$),$ what is the maximum value of dBC such that the first car has passed C when the second car passes B$?$