I am having trouble figuring out how to start the math part of this crime scene scenario

Question

You and your team of investigative specialists have been called out to a case. You and the coroner arrive at the scene. There is a body, foot prints, and obvious signs of a struggle. Let’s look at the evidence:

1. The Body
2. The coroner tells you that at 5pm the temperature of the body is 84°F. They also tell you that the temperature of the room is 72°F. One hour later, the body temperature registers 80°F. Assume an average body temperature of 98.6°F.
3. The Foot Prints
4. Distinct footprints are found that don’t match the victim’s, leading to and from the location of the murder. They are marked on the map attached. Using the scale on the grid lines, complete the following two tables:

Path 1
x	y
Path 2
x	y

Use the evidence listed above to determine when the body was killed and where the body was found.

After viewing security footage, you find 3 suspects to be questioned. Here’s what they had to say at 11:30pm:

1 https://www.facebook.com/pg/csimiamicsilasvegascsiny/videos/

Group Number _____________________ Course & Section _____________________ Date _____________________

1. Suspect 1
2. “Yeah, I work downtown. I work the lunch-early dinner shift at Carlos Poco Loco, 10am-4:30pm. We don’t open until 11am, but someone has to clean and stock. I get a 30 minute lunch break, but I have to stay here if I want the free food. I go to Fricker’s all the time, but I had nothing to do with a murder!”
3. Suspect 2
4. “Where do I work? I work at McDonald’s. ... No, the other one. ... No, the OTHER one. On Front Street & Main. I work the breakfast shift. ... Well, it’s open 24 hours, so I’m scheduled 6am to 2pm. ... No, I live on the East Side. Why would I cross the river? ... Oh, well I did go to the Bird. We sat outside and celebrated a birthday.”
5. Suspect 3
6. “No, I don’t work downtown, but I had the day off. I went to the Glass Outlet, looking for new stemware. ... Well, then I walked down for a late lunch at Registry Bistro. ... Oh, I probably left there about 2:30, 3:00. Why?”

Using ONLY the presented data, and assuming all suspects can be confirmed to be where they said when they said, write a letter (at least 1⁄2 page in length) to the new DA explaining your methods, what equations you used, the background on those equations (yes, you must cite your sources!!!), and what information you calculated and found. Then, using your information, explain to the new DA which suspect or suspects should be investigated further and why.

In order for your project to be complete, your group must submit the answers to the above questions/statements, typed, along with your completed letter.

I can email the map picture with the footprints on it as it wont let me copy and paste to this form.

https://www.google.com/maps/@41.649074,-83.5379928,993m/data=!3m1!1e3

Answer 1

You can start with Newton's law of cooling, solving that differential equation will give you the time of the crime.