The temperature of a pan of hot water varies according to newton's law of cooling: dt dt equals negative k times the quantity t minus a , where t is the water temperature, a is the room temperature, and k is a positive constant. if the water cools from 90°c to 85°c in 1 minute at a room temperature of 30°c, how long (to the nearest minute) will it take the water to cool to 60°c?