$1$ Consider the car$-$caravan analogy from Section $4$ in Chapter $1$ of Computer Networking: A Top$-$Down Approach. In this problem, assume a propagation speed of $50$ km$/$hr and that each toll booth takes $6$ seconds to service a car.

a$)(7$ points$)$ Suppose the caravan of $10$ cars begins immediately in front of the first toll booth, travels $20$ km to a second toll booth, then another $30$ km to a third toll booth, and finally stops immediately after the third tool booth. Thus, they travel a total of $50$ km$.$ What is the total end$-$to$-$end delay?

b$)(3$ points$)$ Where is the last car in the caravan after one hour? Your answer must include a distance$/$specific location, and not only a relative direction.