First, we need to determine Rubio's walking speed in miles per minute.
He can walk \( \frac{2}{3} \) of a mile in 16 minutes. To find his speed in miles per minute, we can calculate:
\[ \text{Speed} = \frac{\frac{2}{3} \text{ miles}}{16 \text{ minutes}} = \frac{2}{3 \times 16} = \frac{2}{48} = \frac{1}{24} \text{ miles per minute} \]
Next, we need to find out how long it takes him to walk 1 mile at this speed. We can set up the equation:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{1 \text{ mile}}{\frac{1}{24} \text{ miles per minute}} \]
To calculate this, we can simplify:
\[ \text{Time} = 1 \times 24 = 24 \text{ minutes} \]
Thus, it will take Rubio 24 minutes to walk to his friend's house.