Integral Intermediate

Problem - 4565

According to Newtonâ€™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?

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