Math whiz needed! (in Contests)

For 2,802 Explosive Shots and $50,000

Your friend was killed in his apartment, and his original body temperature was 98.6 degrees F. When paramedics arrived, they tested his body and found that his internal temperature was 92.6 degrees. The room was set to a constant 70 degrees. You are a mathematician hired by the police force to investigate. Assuming that K (A part of the equation, because you already know the formula that is needed) is equal to exactly .1177284058, and the police assume that the maximum speed the suspect could have escaped the area is 90 mph, what is the search radius that you should tell the policemen to set? Also, your math is so good that you solve the problem instantly. First one to post to area of the place in which the circle should take place in will win the prizes.

"First one to post to area of the place in which the circle should take place in will win the prizes."

I can't decipher that sentence.

"First one to post the area of the circle in which the search should take place will win the prizes."

Thanks for that, I can be a bit short-sighted sometimes.

this is a wild guess and most likely is wrong..but 4450.12 miles

3.2 miles.

Both wrong: will check in the morning to see if anyone has gotten it.

Rewrite it into metric, and I'll give it a try...

From newton's law of cooling:
T(t) = Tr + (Ti - Tr)*exp(-.1177284058t)

plugging in numbers a solving for t gives t=2.
If t is measured in hours, then
90mph * 2h = 180 mi
180^2 * pi = 101787 mi^2

Booo! Diffusion but there's no area to the room

Typically, K is measured in cm^2 / hr. That really throws stuff off.

Here's an implicit solution:

(90 miles * ln(.79 degrees F) / K)^2 * Pi

Sorry, put a negative sign on the outside of that whole thing.

Miandrital, that answer only works if K is measured in mi^2 / hr. Like I said, it's usually cm^2 / hr, which makes for a very odd K value. The resultant area of the circle is:

68279514367512021374618114.568246 miles.

Nice.

th00p, units are important in your initial question.

K is just the cooling rate, it has no dependence on distance.
The units of K are 1/hr.

He died of natural death no search needed lol

Depends if you're in America or not.

Wouldn't the police just grab the first dodgy looking character on the street outside and arrest him?

With the K, you calculate at what time the victim died.

With the maximum speed you calculate the maximum possible distance the killer would be able to travel.

Though the police usually assumes wrong, because you can easily catch a plane to fly far far away :)

If the murder was so premeditated that you have a flight ready within 2 hours of killing somebody, I am sure you will probably leave behind a paper trail a mile long for the police to follow.

i would say 10.70151208722 miles
if i was the killer i would take the body and hide it so the cops cant find it, why leave it there and get caught

could also be 642.0907252332 miles

450 miles in diameter.

Which did you want: what is the search radius that you should tell the policemen to set? or First one to post the area?

385.714 square miles.

not really that good at math, but this is a guess, based upon how long it took the body temperature to drop

98.6-92.6=6 degree drop

6/1.4 degree drop per hour=4.2857

4.2857 hours since death * 90mph = 385.714 square miles

"98.6-92.6=6 degree drop

6/1.4 degree drop per hour=4.2857

4.2857 hours since death * 90mph = 385.714 square miles"

The last calculation is wrong, but assuming the first two are correct:

Radius of search Circle = 4.2857 hours * 90 mph = 385.714 miles
Area of Circle to Search = Pi*r^2 = Pi*385.714^2 = 467,391 miles^2

So, you would have to search an area that was 467,391 square miles, which is roughly two times the size of Texas. Good luck with that.

1) Miandrital's first answer is right. I will be sending him the money and ex shots soon.

2) bartjan, sorry, although I should have changed it to metric the thought never crossed my mind... next contest I will.

3) Yes I did forget to say that K is in a K/hr format, but it does NOT get measured in mi^2/hr or cm^2/hr, as it is the rate at which the body is cooling. Also this wouldn't make sense as NOTHING in Newton's Law of Cooling has to do with distance.


Great job on this, keep your eyes out I may have some more topics like this out there for you guys in the future!

3b) Also should have noted that t is in hours, not minutes or days, for those who are keeping track.

For a start, the fact you need to know the Law of Cooling makes this Physics/Chemistry and not Math.
Math may give situations in the questions but only ones in which you can use equations that are originally given for use with graphs and such, Physics and Chemistry equations always use a situation.
Just thought to make a point of that so no future mistakes are made about subject.

Whoa.

Okay, well I was taught this in math class, and I thought physics was only involving motion and the way things move through the world. I also thought chemistry was using chemical reactions and the likes, but then again I've been wrong many times before. This probably should read "Forensic Scientist needed!" anyways, but hey it's not that big a deal to me.

Lol, wonder why they would teach that in Mathematics?
Maths is the manipulation of number for statistic purposes or to measure length, width, breadth or time.
Yes, this is there for measurement but Mathematics never require you to know equations as situation specific as that.
This should be Chemistry related imo since it is related to a rate of reaction :)

Newton's Law of cooling was taught first to me in Chemistry AP (Freshman Year), then Trig (Sophomore year) and again in Calc (Junior year - currently enrolled in)

So yes, this is math, as well as chemistry and physics.

And Yay for Newton's law of cooling! :D

Newton was a baller.