A forensic scientist arrives at a flat where a person has been found dead…

A forensic scientist arrives at a flat where a person has been found dead. The room is kept at a steady $18\ ^\circ\text{C}$ by a thermostat. At $17{:}00$ the body temperature is $29\ ^\circ\text{C}$, and at $19{:}00$ it is $24\ ^\circ\text{C}$. The scientist assumes that the body cooled by Newton's law from its normal temperature of $37\ ^\circ\text{C}$ at the moment of death, with the same constant $k$ throughout. She first finds $k$ from the two readings. She then uses $k$ to work back to the time of death and to predict what the thermometer will show later. Find $k$ in per hour, the time in hours from the death to the reading at $17{:}00$, and the body temperature at $21{:}00$ in degrees Celsius. State the time of death to the nearest minute.