To find out how far Joey is from home, we need to calculate his net distance traveled. Joey started by walking east (positive direction) and then walked west (negative direction). We will combine these distances to determine his final position relative to home.
Firstly, let's write the distances as improper fractions for easier calculations:
- \(15 \frac{2}{3}\) meters is:
\[
15 \frac{2}{3} = 15 + \frac{2}{3} = \frac{45}{3} + \frac{2}{3} = \frac{47}{3}
\]
- \(21 \frac{3}{4}\) meters is:
\[
21 \frac{3}{4} = 21 + \frac{3}{4} = \frac{84}{4} + \frac{3}{4} = \frac{87}{4}
\]
Now, convert both fractions to a common denominator. The least common denominator (LCD) of 3 and 4 is 12.
Convert \(\frac{47}{3}\) to a denominator of 12:
\[
\frac{47}{3} = \frac{47 \times 4}{3 \times 4} = \frac{188}{12}
\]
Convert \(\frac{87}{4}\) to a denominator of 12:
\[
\frac{87}{4} = \frac{87 \times 3}{4 \times 3} = \frac{261}{12}
\]
Now subtract the two fractions, since walking west is in the negative direction:
\[
\frac{188}{12} - \frac{261}{12} = \frac{188 - 261}{12} = \frac{-73}{12}
\]
The fraction \(\frac{-73}{12}\) represents the negative distance west from home, meaning Joey is 73/12 meters west of home.
Convert \(\frac{73}{12}\) to a mixed number:
\[
\frac{73}{12} = 6 \frac{1}{12}
\]
Thus, Joey was \(6 \frac{1}{12}\) meters west from home. The "negative" direction indicates west, but since the problem asks for how far Joey is from home, we report the distance without direction:
Joey was \(6 \frac{1}{12}\) meters from home.
Joey walked east for 15 2/3 meters from home. Then, he walked west for 21 3/4 meters. How far was Joey from home? Write your answer as a mixed number only.
Joey was __ meters from home.
1 answer