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The problem involves calculating how many miles Josiah has left to run in a marathon. Here's a breakdown of the information:

1. The marathon is \( 26 \frac{1}{5} \) miles long.
2. At \( 4 \frac{1}{4} \) miles from the start, Josiah meets his wife.
3. He runs another \( 9 \frac{1}{2} \) miles further to meet his friends.
4. We need to calculate how many miles he has left after meeting his friends.

### Step-by-Step Solution:

1. **Convert the mixed numbers into improper fractions:**
   - \( 26 \frac{1}{5} = \frac{131}{5} \) (since \( 26 \times 5 + 1 = 131 \))
   - \( 4 \frac{1}{4} = \frac{17}{4} \)
   - \( 9 \frac{1}{2} = \frac{19}{2} \)

2. **Add the distance Josiah has run so far (after meeting his friends):**
   - He has already run \( 4 \frac{1}{4} + 9 \frac{1}{2} \).
   - First, find a common denominator for \( \frac{17}{4} \) and \( \frac{19}{2} \), which is 4:
     - \( \frac{17}{4} + \frac{38}{4} = \frac{55}{4} \).

3. **Subtract the distance run from the total marathon distance:**
   - Total distance \( 26 \frac{1}{5} = \frac{131}{5} \).
   - Convert \( \frac{131}{5} \) and \( \frac{55}{4} \) to have a common denominator (which is 20):
     - \( \frac{131}{5} = \frac{524}{20} \)
     - \( \frac{55}{4} = \frac{275}{20} \)
     - Now subtract \( \frac{275}{20} \) from \( \frac{524}{20} \):
       - \( \frac{524}{20} - \frac{275}{20} = \frac{249}{20} \).

4. **Convert the result back to a mixed number:**
   - \( \frac{249}{20} = 12 \frac{9}{20} \).

So, Josiah has \( 12 \frac{9}{20} \) miles left to run.

Would you like further details or clarifications?

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Here are 5 related questions to expand your understanding:
1. How do you convert mixed numbers into improper fractions?
2. How do you find a common denominator for two fractions?
3. What steps are involved in converting an improper fraction back into a mixed number?
4. How can we apply these concepts to other real-world distance problems?
5. How do you subtract fractions with different denominators?

**Tip:** Always make sure to convert mixed numbers into improper fractions before performing arithmetic operations like addition or subtraction.

Josiah is running a marathon which is 26 1/5 miles long. At 4 1/4 miles from the start, he meets his wife. He runs another 9 1/2 miles further. How many miles does Josiah have left to run?

Learn how to calculate the remaining distance in a marathon by subtracting mixed fractions. This problem involves converting mixed numbers to improper fractions and finding a common denominator. Suitable for students in Grades 6-8.

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