5.18 How many police cars? (This problem has been adopted from a real-world situation.) The police department of a medium-sized city recently decided to expand police services and, among other things, placed two additional patrol cars in the streets (over and above those they already had) on a 24-hour-a-day basis. Both before and after the addition of the two cars, it was found that each car on the streets was responding to about one call every 2 hours (apparently the total number of calls also increased somewhat) and that the mean service time for a call was about 30 minutes. It was also found that in the first 4 months after the addition of the two new cars, the average travel time to a call was 5.28 minutes. Before the addition of the two cars it was 5.82 minutes. The police dispatcher, throughout this time, was sing an approximate closest-available-car dispatching strategy ("approximate" because the dispatcher does not know the exact position of every police car at all times).
Based on this information can you guess approximately how many patrol cars this city's police department was fielding before the addition of the two new patrol cars ?
Hint: One of the coauthors, with essentially the same information as you have (but not quite as neatly presented) guessed "12 or 13," using the techniques of Section 5.8. The right answer turned out to be 13!