First, let's determine Rubio's walking rate in miles per minute. He can walk \( \frac{2}{3} \) miles in 16 minutes.
To find his rate in miles per minute:
\[ \text{Rate} = \frac{2/3 \text{ miles}}{16 \text{ minutes}} = \frac{2}{3} \div 16 = \frac{2}{3} \times \frac{1}{16} = \frac{2}{48} = \frac{1}{24} \text{ miles per minute} \]
Now that we know his walking rate is \( \frac{1}{24} \) miles per minute, we need to calculate how long it will take him to walk 1 mile.
Using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Rate}} \]
Substituting the known values:
\[ \text{Time} = \frac{1 \text{ mile}}{\frac{1}{24} \text{ miles per minute}} = 1 \times 24 = 24 \text{ minutes} \]
Thus, it will take Rubio 24 minutes to walk to his friend's house.