To find out how long it will take Rubio to walk one mile to his friend's house at a pace of \(\frac{2}{3}\) miles in 16 minutes, we first need to determine his walking speed.
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Determine walking speed: \[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{\frac{2}{3} \text{ miles}}{16 \text{ minutes}} = \frac{2}{3} \div 16 = \frac{2}{3} \times \frac{1}{16} = \frac{2}{48} = \frac{1}{24} \text{ miles per minute} \]
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Calculate the time to walk one mile: \[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{1 \text{ mile}}{\frac{1}{24} \text{ miles per minute}} = 1 \times 24 = 24 \text{ minutes} \]
Therefore, it will take Rubio 24 minutes to walk to his friend's house.