Paul VI High School
901 Hopkins Rd., Ste. B
Haddonfield, NJ 08033
December 4, 2018
Big City Police Department
Constabulary Avenue
Big City, PU 11235
Dear Officer:
The letter you sent to me last month has been carefully read and weighted. Firstly, please send my condolences for this police officer’s death to his family. As for the hinders you encountered in this case, I may provide you with something meaningful which can effectively address your problems. I have conducted some investigation based on the alibi of the suspect during this time which can probably solve your puzzles respectively. My analyses are presented below in responding to your request. Please take them serious into account.
Firstly, as for your first query that why Mr. Amazing didn’t arrive Big City earlier if she traveled so fast, my dear officer, Mr. Amazing could definitely arrive the Big City much earlier and even earlier than the interception by you if she did travel at 35mph average speed as Sheriff Gocher put it. But why Mr. Amazing would deliberately delay her time of escaping? It doesn’t make any sense. Let’s look back at the travel speed of Mr. Amazing calculated by Sheriff Gocher. Through my investigation, I find Sheriff Gocher had made a serious mistake in calculating it. We already know each transportation’s traveling speed (V1,V2 and V3) and every stage’s length. Then we can calculate the traveling time (T1,T2 and T3) of each stage: T1=S1÷V1=(h); T2=S2÷V2 =(h); T3=S3÷V3=(h). Assuming that Mr. Amazing made connections between them without any delay, we can get the minimum traveling time (T) of Mr. Amazing: = T1+T2+ T3. We also know that the total distances (S) between Sure Thing and Big City is: S=12+12+12=36 (miles). Therefore, the average traveling speed () should be: = =36÷(++)≈20.17 (mph)<35 (mph). The recalculated statistics show that Sheriff Gopher overrate the traveling speed of Mr. Amazing for nearly 15mph. As we can learn from the above, the minimum traveling time (T) is nearly 1.78 hours, so it is likely that Mr. Amazing traveled for 2 hours between two cities if taking delays into account.
As I concluded above, the traveling speed of Mr. Amazing have been recalculated to nearly 20mph, and the time for Mr. Amazing to travel between two countries is at least 1.78h. These statistics can solve your second query which is concerning about how Mr. Amazing use her time of journey to counter the Gocher’s argument. Since the poor Doornail were found alive by a donut vendor at 11:11 a.m., and then was absent for his daily 12:12 coffee, finally was found dead at 12:15 p.m., we can deduct that death time is between 11:11a.m. and 12:15 p.m.. As she was intercepted by you at 12:56 p.m., and if is the case that it is her who stabbed Doornail, the time left for her to travel is more than Tmin=12:56-11:11=1 hour and 44 minutes, and less than Tmax=12:56-12:15= 41 minutes. Since the it needs at least 1.78 hours for Mr. Amazing to travel to Big City, she should depart Sure Thing at least before Tdeparture=12:56-1:47=11:09 which is a bit earlier than the time Doornail was killed. This evidence suggests that the judgment of Sheriff Gopher may not be right.
Last but not least, as for your last question about who was twisting the facts, I suppose you can tell by yourself from the former analyses of this letter. But still let me put it more clear, through the exact calculation, I found that Sherriff Gocher was twisting the facts either on purpose or unwittingly, and Mr. Amazing might be innocent. Gopher made the mistakes since he wrongly calculated the traveling time between two cities. The average velocity can’t be simply evenly divided even if the traveling spaces are the same. Since Gopher mistakes at the beginning, his further assumption is also wrong. Sheriff Gopher may be blinded by his grief for his man. Mr. Amazing was not in the midst of the crime scene, on the contrary, she had left the Sure Thing before Doornail’s death.
In conclusion, I strongly suggest you to release Mr. Amazing immediately because she is innocent. However, since the murder is still on the lam, my dear officer, you need to broad your criminal suspects including Mr. Gopher, since his assertion showed strong hostility to Mr. Amazing. Although Mr. Amazing did not get along well with Sure Thing police and had an argument with the dead, it is not an excuse for us to jump into conclusion that she is guilty since the evidence I provide above clearly testify her innocence.
Yours sincerely,
Hezhu Zhang
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