Question

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

Answer 1

To find out how far Joey is from home after walking east and then west, we begin by calculating the total distance he walked in each direction.

1. Joey walked east: \( 15 \frac{2}{3} \) meters.
2. Joey walked west: \( 21 \frac{3}{4} \) meters.

First, we convert the mixed numbers into improper fractions to make calculations easier.

For \( 15 \frac{2}{3} \):
\[
15 \frac{2}{3} = \frac{15 \times 3 + 2}{3} = \frac{45 + 2}{3} = \frac{47}{3}
\]

For \( 21 \frac{3}{4} \):
\[
21 \frac{3}{4} = \frac{21 \times 4 + 3}{4} = \frac{84 + 3}{4} = \frac{87}{4}
\]

Next, we need to find the total distance Joey is from home after both walks. Since he walked east first and then west, we subtract the eastward distance from the westward distance:

\[
\text{Total distance from home} = \text{Distance walked west} - \text{Distance walked east}
\]
\[
\text{Total distance from home} = \frac{87}{4} - \frac{47}{3}
\]

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

Now we convert each fraction:
\[
\frac{87}{4} = \frac{87 \times 3}{4 \times 3} = \frac{261}{12}
\]
\[
\frac{47}{3} = \frac{47 \times 4}{3 \times 4} = \frac{188}{12}
\]

Now we subtract the two fractions:
\[
\frac{261}{12} - \frac{188}{12} = \frac{261 - 188}{12} = \frac{73}{12}
\]

Finally, we convert \( \frac{73}{12} \) back to a mixed number:
\[
73 \div 12 = 6 \quad \text{(remainder 1)}
\]
Thus, \( \frac{73}{12} = 6 \frac{1}{12} \).

Joey was \( 6 \frac{1}{12} \) meters from home.