Joey walked north for 3 1/3 miles and then walked south for 1 1/5 miles. How far is Joey from home? Write your answer as a mixed number only.

Question

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4 1/15 miles
4 8/15 miles
2 2/15 miles
2 1/12 miles

Answer 1

To determine how far Joey is from home, we need to subtract the distance he walked south from the distance he walked north.

1. Convert the mixed numbers to improper fractions:

   • \( 3 \frac{1}{3} = \frac{10}{3} \)
   • \( 1 \frac{1}{5} = \frac{6}{5} \)

2. Subtract the distances: \[ \frac{10}{3} - \frac{6}{5} \]

3. Find a common denominator: The least common multiple of 3 and 5 is 15.

   Convert both fractions: \[ \frac{10}{3} = \frac{10 \times 5}{3 \times 5} = \frac{50}{15} \] \[ \frac{6}{5} = \frac{6 \times 3}{5 \times 3} = \frac{18}{15} \]

4. Now perform the subtraction: \[ \frac{50}{15} - \frac{18}{15} = \frac{50 - 18}{15} = \frac{32}{15} \]

5. Convert \( \frac{32}{15} \) back to a mixed number:

   • Divide 32 by 15, which equals 2 with a remainder of 2.
   • So, \( \frac{32}{15} = 2 \frac{2}{15} \).

Thus, Joey is \( 2 \frac{2}{15} \) miles from home.

Final answer: \( 2 \frac{2}{15} \) miles