Answer: -27/7
Step-by-step explanation:
A) The differential equation comes from the fact that the rate of temperature change is proportional to the difference in temperatures.

B) Find general solution by separating variables and integrating

:
C) Initial condition is t=0, T = 87

D) Total time elapsed is 10 minutes, new temperature is 84

solve for alpha

E) Temperature function is:

solving for t

Plug in T = 98.6

This is approximately 32 minutes before he arrived or about 1:20 AM
Let's the name the first number x and the consecutive number x + 1. The sum of both of these numbers equals to 53.
We now have our equation:
x + x + 1 = 53
Now solve for x.
x + x + 1 = 53
2x + 1 = 53 <-- Combine like terms
2x = 52 <-- Subtract 1 from each side
x = 26
So, the first number is 26 and the second number is 27.