Problem $2$

Consider an $8-$car caravan, where the propagation speed is $100k\frac{m}{?}$ 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 $d_{AB}$ and $d_{BC}$ be the distance between $A-B,$ and $B-C.$

a$)$ Suppose $d_{AB}=d_{BC}=10km.$ 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 $d_{AB}=d_{BC}=100km.$

d$)$ Still suppose $d_{AB}=d_{BC}=100km.$ 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 $d_{BC}$ such that the first car has passed

$C$ when the second car passes $B?$