Calculus Student
Franklin & Marshall College
Lancaster, PA 17604
Dear Calculus Student:
I am the chief detective of the Big City Police Department, and I'm writing to ask if you could help us investigate the alibi of a suspect in a current murder case. The suspect, a Ms. Grace Amazing, is believed to have murdered a police officer; she maintains her innocence despite damaging circumstantial evidence to the contrary.
Ms. Amazing and her ex-husband Jeremy Amazing both reside in Sure Thing, PU. Their divorce was, by all accounts, a bitter one, and as Mr. Amazing works for the Sure Thing Sheriff Department, Ms. Amazing has had her share of run-ins with the local police. The morning of the murder, in fact, Ms. Amazing had argued publicly and loudly with Deputy Dirk Doornail, who had ticketed her for a questionable parking violation. That very same afternoon, Deputy Doornail was found dead, stabbed in the chest by an unknown assailant. He was last seen alive by a donut vendor at 11:11 a.m. (this was part of a daily routine of Doornail, who was a superstitious fellow). His body was found by the same donut vendor at 12:15 p.m., who began searching when Doornail did not show up for his daily 12:12 coffee.
Immediately upon the discovery of Doornail's corpse, hue and cry were raised. It was discovered that Grace Amazing had left Sure Thing headed for Big City; I was immediately warned of her journey. Sure enough, I intercepted her at the Big City trolley station at 12:56 p.m., where I arrested her. Although she has repeatedly denied the murder in fact she claims that she left Sure Thing before the murder took placeshe's currently being held for trial. The Sheriff of Sure Thing, Sheriff Gocher, claims that she could easily have left after the murder, and that the timing of her trip, leaving just as she did, is damning evidence.
In order for you to understand my quandry, I should tell you a bit about the geography of PU. A journey from Sure Thing to Big City requires three stages, each of which is 12 miles long. First, one travels from Sure Thing to Sugar by train (known affectionately to locals as the "Su-Su Train"). From there, one travels across a lake by ferry to the city of Plum. From Plum, there is a trolley which travels across the Absolutely Mountains (and across its famous gorges) into Big City. Each of these legstrain, ferry, and trolleyhas frequent runs, so it's not uncommon to make connections between them without delay.
(By the way, there was quite a celebrated murder case two years ago in these very same Absolutely Gorges, and, in fact, a bunch of enterprising Calculus II students helped convict the murderer! )
As for the current case, Ms. Amazing insists she left Sure Thing long before the murder took place, but we've found no one to corroborate this alibi. On the other hand, Sheriff Gocher argues that she could easily have made the trip in just over an hour. The Su-Su Train travels at 65 mph; the Sugar-Plum Ferry travels at 10 mph, and the trolley goes 30 mph. He points out that because each leg is of equal distance, Grace traveled at an average speed of about 35 mph (i.e., the average of 65, 10, and 30). Since she went a total of 36 miles (three legs of 12 miles each), this places her squarely in the midst of the crime scene (he says).
The reason I'm writing to you is that somethingmy intuition, my instinct, I don't know whattells me that Sheriff Gocher has it in for this poor woman. On the other hand, she doesn't seem overly fond of him, either. I don't know which side to believe, but I don't know how to discredit the argument of either side, either. How could it have taken her so long if her average speed was 35 mph? And if her journey really did take her two or three hours, then how can she counter Gocher's argument? Which of these two folks is twisting the facts, and how?
If you could help me solve this perplexing riddle, say before September 14 when the preliminary hearing is scheduled, I'd be most grateful to you.
See "The Case of the Crushed Clown" for more details.
|
