To find out how far Roberto needs to walk on the second day, we first need to determine how much distance he has left to cover after walking on the first day.
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Convert the total distance of the block into an improper fraction: \[ \text{Total distance} = 1 \frac{3}{4} \text{ miles} = \frac{7}{4} \text{ miles} \]
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Determine how far Roberto has walked on the first day: \[ \text{First day distance} = \frac{5}{8} \text{ miles} \]
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Calculate the remaining distance to walk on the second day: We need to subtract the distance walked on the first day from the total distance of the block: \[ \text{Remaining distance} = \text{Total distance} - \text{First day distance} = \frac{7}{4} - \frac{5}{8} \]
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To perform this subtraction, we need a common denominator. The least common multiple of 4 and 8 is 8. Convert \(\frac{7}{4}\) to an equivalent fraction with a denominator of 8: \[ \frac{7}{4} = \frac{7 \times 2}{4 \times 2} = \frac{14}{8} \]
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Now we can subtract: \[ \text{Remaining distance} = \frac{14}{8} - \frac{5}{8} = \frac{14 - 5}{8} = \frac{9}{8} \]
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Convert the remaining distance back to a mixed number for easier understanding if needed: \[ \frac{9}{8} = 1 \frac{1}{8} \text{ miles} \]
Therefore, Roberto needs to walk \(\frac{9}{8}\) miles, or 1 1/8 miles, on the second day to finish picking up trash in his neighborhood.
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