According to Newton’s law of cooling, the rate at which a cup of coffee cools is proportional to the difference between its temperature and that of the room it is in. A certain cup of coffee cools from $164^{\circ}$ to $140^{\circ}$ (all temperatures Fahrenheit) in five minutes, and then from $140^{\circ}$ to $122^{\circ}$ in the next five minutes. What is the temperature of the room?