Math Problem Statement

Ali decided to camp last weekend. He wanted to walk from his house to the campsite, which is 8 5/8 miles away. Therefore, he left his house at 6 am. At 6:30 am, Ali found that he was 5 1/3 miles away from the campsite. How far did Ali walk so far?

Solution

To determine how far Ali has walked so far, we subtract the distance remaining from the total distance.

  1. Total distance to the campsite: 858=6988 \frac{5}{8} = \frac{69}{8} miles.
  2. Distance remaining from the campsite: 513=1635 \frac{1}{3} = \frac{16}{3} miles.

To subtract these, we first find a common denominator for 698\frac{69}{8} and 163\frac{16}{3}. The least common denominator is 24.

  • Convert 698\frac{69}{8}: 698=20724\frac{69}{8} = \frac{207}{24},
  • Convert 163\frac{16}{3}: 163=12824\frac{16}{3} = \frac{128}{24}.

Now subtract: 2072412824=7924.\frac{207}{24} - \frac{128}{24} = \frac{79}{24}.

Simplify 7924\frac{79}{24}:

  • 7924=3724\frac{79}{24} = 3 \frac{7}{24}.

Ali walked 37243 \frac{7}{24} miles so far.

Would you like further clarification or have questions?

Related Questions:

  1. How much farther does Ali need to walk to reach the campsite?
  2. At what speed was Ali walking if it took him 30 minutes to cover this distance?
  3. What fraction of the total distance has Ali covered so far?
  4. How would the calculation change if Ali's house were farther?
  5. Can this be converted into kilometers if needed?

Tip: Always convert mixed fractions into improper fractions to simplify calculations.

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Math Problem Analysis

Mathematical Concepts

Fractions
Subtraction
Distance Calculation

Formulas

Distance covered = Total distance - Remaining distance

Theorems

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Suitable Grade Level

Grades 5-7