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: $$73÷12=6\text{ R }1$$ 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.