Question

A policeman cruises (on average) approximately ten minutes before stopping a car for speeding. 90 % of the cars stopped are given speeding tickets with an $80 fine. It takes the policeman an average of five minutes to write such a ticket. The other 10 % of the stops are for more serious offenses, leading to an average fine of $300. These more serious charges take an average of 30 minutes to process. In the long run, at what rate (in dollars per minute) does he assign fines.

Answer 1

Answer:

$5.83 per minute

Explanation:

Assuming that the policeman cruises for 10 minutes before each stop, total time for a stop can take 15 minutes (speeding) or 40 minutes (serious charges). The average time per stop is:

$t = 15*0.9+40*0.10\\t=17.5\ minutes$

If 90% of the fines are for $80 and 10% of fines are for $300, the average value of fines is:

$V= 0.9*\ 80+0.1*\ 300\\V=\ 102$

The rate, in dollars per minute is:

$r=\frac{V}{t}=\frac{\ 102}{17.5}\\ r=\ 5.83/min$

The rate is $5.83 per minute.