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

Answer 1

To find out how far Joey is from home after walking, we first need to calculate the total distance he walked north and south.

1. Joey walked north for \( 3 \frac{1}{3} \) miles. In improper fraction form, this is: \[ 3 \frac{1}{3} = \frac{10}{3} \text{ miles} \]

2. Next, he walked south for \( 1 \frac{1}{5} \) miles. In improper fraction form, this is: \[ 1 \frac{1}{5} = \frac{6}{5} \text{ miles} \]

Now, we need to find the net distance from home:

3. Since he walked north and then south, we subtract the distance walked south from the distance walked north: \[ \text{Net distance} = \text{Distance north} - \text{Distance south} = \frac{10}{3} - \frac{6}{5} \]

4. To subtract these fractions, we need a common denominator. The least common multiple of 3 and 5 is 15. We convert both fractions: \[ \frac{10}{3} = \frac{10 \times 5}{3 \times 5} = \frac{50}{15} \] \[ \frac{6}{5} = \frac{6 \times 3}{5 \times 3} = \frac{18}{15} \]

5. Now we can subtract: \[ \frac{50}{15} - \frac{18}{15} = \frac{50 - 18}{15} = \frac{32}{15} \]

6. Now we'll convert \( \frac{32}{15} \) into a mixed number: \[ 32 \div 15 = 2 \quad \text{remainder} \quad 2 \] Thus, \[ \frac{32}{15} = 2 \frac{2}{15} \]

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

The answer is: \[ \boxed{2 \frac{2}{15}} \]