A cup of soup cools from $80\ ^\circ\text{C}$ to $70\ ^\circ\text{C}$ in $5.0$ minutes in a room at $20\ ^\circ\text{C}$. Using the average temperature in each interval, how long does it take to cool from $70\ ^\circ\text{C}$ to $60\ ^\circ\text{C}$?