Question

Joey left home on a walk. He walked EAST for 15 2/3 meters from home. Then, he walked back WEST for 21 3/4 meters. How far was Joey from home?

Answer 1

To find out how far Joey is from home after his walk, we need to calculate his total displacement by considering the distances he walked in each direction.

1. **Walking East**: Joey walked \(15 \frac{2}{3}\) meters. To convert this to an improper fraction:
\[
15 \frac{2}{3} = 15 + \frac{2}{3} = \frac{15 \times 3 + 2}{3} = \frac{45 + 2}{3} = \frac{47}{3} \text{ meters}
\]

2. **Walking West**: Then, Joey walked \(21 \frac{3}{4}\) meters back. Converting this to an improper fraction:
\[
21 \frac{3}{4} = 21 + \frac{3}{4} = \frac{21 \times 4 + 3}{4} = \frac{84 + 3}{4} = \frac{87}{4} \text{ meters}
\]

3. **Calculating the Total Displacement**:
- When Joey walks East (positive direction), we add the distance.
- When he walks West (negative direction), we subtract the distance.

So, the total displacement from home can be calculated as:
\[
\text{Total Displacement} = \text{East} - \text{West}
= \frac{47}{3} - \frac{87}{4}
\]

To perform this subtraction, we need a common denominator. The least common multiple of \(3\) and \(4\) is \(12\).

Converting both fractions to have a denominator of \(12\):
- For \(\frac{47}{3}\):
\[
\frac{47}{3} = \frac{47 \times 4}{3 \times 4} = \frac{188}{12}
\]
- For \(\frac{87}{4}\):
\[
\frac{87}{4} = \frac{87 \times 3}{4 \times 3} = \frac{261}{12}
\]

Now we can subtract:
\[
\text{Total Displacement} = \frac{188}{12} - \frac{261}{12} = \frac{188 - 261}{12} = \frac{-73}{12}
\]

The negative sign indicates that Joey is \(73/12\) meters to the WEST of home.

4. **Converting the Displacement to Mixed Number**:
\[
73 \div 12 = 6 \text{ R } 1
\]
Thus, \(\frac{73}{12} = 6 \frac{1}{12}\) meters.

So, after all calculations, Joey is **6 \( \frac{1}{12} \) meters** from home, and specifically, he is **6 \( \frac{1}{12} \) meters WEST** of his starting point.