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 $200^{\circ} \mathrm{F}$ when freshly poured, and $1 \mathrm{~min}$ later has cooled to $190^{\circ} \mathrm{F}$ in a room at $70^{\circ} \mathrm{F}$, determine when the coffee reaches a temperature of $150^{\circ} \mathrm{F}$.
 6.07