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