To find out how far Joey is from home after his walk, we will calculate the total distance he walked in each direction and then determine his final position relative to home.
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Walking East:
- Joey walked \( 15 \frac{2}{3} \) meters east.
- Converting \( 15 \frac{2}{3} \) to an improper fraction: \[ 15 \frac{2}{3} = \frac{15 \times 3 + 2}{3} = \frac{45 + 2}{3} = \frac{47}{3} \text{ meters} \]
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Walking West:
- Joey then walked \( 21 \frac{3}{4} \) meters west.
- Converting \( 21 \frac{3}{4} \) to an improper fraction: \[ 21 \frac{3}{4} = \frac{21 \times 4 + 3}{4} = \frac{84 + 3}{4} = \frac{87}{4} \text{ meters} \]
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Finding the net distance from home:
- We need to find the difference in the distances Joey walked. He walked east first, then west. Thus, his overall movement can be calculated as: \[ \text{Total distance from home} = \text{Distance West} - \text{Distance East} \] This can be represented as: \[ d = \frac{87}{4} - \frac{47}{3} \]
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Finding a common denominator:
- The least common multiple (LCM) of 4 and 3 is 12.
- Convert each fraction: \[ \frac{87}{4} = \frac{87 \times 3}{4 \times 3} = \frac{261}{12} \] \[ \frac{47}{3} = \frac{47 \times 4}{3 \times 4} = \frac{188}{12} \]
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Calculating the difference: \[ d = \frac{261}{12} - \frac{188}{12} = \frac{261 - 188}{12} = \frac{73}{12} \]
Thus, the distance Joey is from home, after both legs of his walk, is \( \frac{73}{12} \) meters.
- Converting to mixed number: \[ \frac{73}{12} = 6 \frac{1}{12} \text{ meters} \]
Joey is \( 6 \frac{1}{12} \) meters away from home.
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