To find out how long it will take Sarah to walk 1 mile to her friend's house at her current walking rate, we first need to determine how many minutes she takes to walk 1 mile based on her walking speed.
Sarah can walk \( \frac{2}{3} \) of a mile in 16 minutes. We can find her walking speed in miles per minute:
\[ \text{Speed} = \frac{\frac{2}{3} \text{ miles}}{16 \text{ minutes}} = \frac{2}{3 \times 16} = \frac{2}{48} = \frac{1}{24} \text{ miles per minute} \]
Next, we want to know how long it takes her to walk 1 mile. Since she walks at a rate of \( \frac{1}{24} \text{ miles per minute} \), the time \( t \) it will take her to walk 1 mile is given by:
\[ t = \frac{\text{Distance}}{\text{Speed}} = \frac{1 \text{ mile}}{\frac{1}{24} \text{ miles per minute}} = 1 \times 24 = 24 \text{ minutes} \]
Therefore, it will take Sarah 24 minutes to walk to her friend's house.