Question 375902
A forensic specialist took the temperature of a victim's body lying in a street
 at 2:10 a.m. and found it to be 85.7'F.
 At 2:40 a.m., the temperature of the body was 84.8'F.
 When was the murder committed if the air temperature during the night was 55'F?
 [Remember, normal body temperature is 98.6'F.] 
:
Find the body temp loss rate in 30 min, convert to degrees/hr
85.7 - 84.8 = .9 * 2 = 1.8 degrees/hr
:
Let t = no. of hrs from 98.6 (temp at death) until temp = 84.8
98.6 - 1.8t = 84.8
-1.8t = 84.8 - 98.6
-1.8t = -13.8
t = {{{(-13.8)/(-1.8)}}}
t = 7.67 hrs or 7 hr 40 min prior to 2:40 am
That would place the time at 7 pm on the previous day