stuck on a diff eq problem

[djk123]

Ok so I've thought about this one for a while but I seem to be stuck. It seems like there isn't enough information, but I'm probably just dumb.

"Sherlock Holmes and Dr. Watson discover the body of a recently deceased homicide victim. At 10:00 PM sharp, Watson records the victim's body temperature to be 31 degrees Celsius and makes a similar recording of 29 degrees Celsius exactly one hour later... Determine to the nearest second the exact time of the murder."

It says to assume the guy's body temperature was 37 Celsius and that the room is always maintained at 15 Celsius.

So you set it up like

dT/dt=k(T-15) where T is temp of body at time t

through separation of variables and integrating I get

T=Ae^(kt) + 15. then plugging in T(0)=37 I get A to be 22 so

T=22e^(kt) + 15.

I think i need to find k but I don't see how the given temperature recordings help me since I don't know when 10 PM was in relation to when the guy died. Any help would be appreciated.