To find out how far Joey is from home, we can determine the net distance he walked.
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Convert the mixed numbers to improper fractions:
- For the distance walked east: \[ 15 \frac{2}{3} = \frac{15 \times 3 + 2}{3} = \frac{45 + 2}{3} = \frac{47}{3} \]
- For the distance walked west: \[ 21 \frac{3}{4} = \frac{21 \times 4 + 3}{4} = \frac{84 + 3}{4} = \frac{87}{4} \]
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Convert to a common denominator: The least common multiple of 3 and 4 is 12.
- Convert \(\frac{47}{3}\): \[ \frac{47}{3} = \frac{47 \times 4}{3 \times 4} = \frac{188}{12} \]
- Convert \(\frac{87}{4}\): \[ \frac{87}{4} = \frac{87 \times 3}{4 \times 3} = \frac{261}{12} \]
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Subtract the distances: Since he walked east (positive direction) and then west (negative direction), we will subtract: \[ \text{Net distance} = \frac{188}{12} - \frac{261}{12} = \frac{188 - 261}{12} = \frac{-73}{12} \] The negative sign indicates the direction, but we are interested in the distance from home, which is the absolute value: \[ \text{Distance from home} = \frac{73}{12} \]
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Convert \(\frac{73}{12}\) back to a mixed number:
- Divide 73 by 12: \( 73 \div 12 = 6 \) remainder \( 1 \)
- Thus, this gives us \( 6 \frac{1}{12} \).
So, Joey was \( 6 \frac{1}{12} \) meters from home.
The final answer is: Joey was \( 6 \frac{1}{12} \) meters from home.
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