Newton's law of cooling states that the temperature of an object changes at a rate proportional to the difference between its temperature and that of its surroundings. Suppose that the temperature of a cup of coffee obeys Newton's law of cooling. If the coffee has a temperature of $210$ degrees Fahrenheit when freshly poured, and $1.5$ minutes later has cooled to $195$ degrees in a room at $78$ degrees, determine when the coffee reaches a temperature of $155$ degrees.
The coffee will reach a temperature of $155$ degrees in minutes.