https://file.aiquickdraw.com/mathbot/file/1726361493006y2hbem0i.jpg

The problem from the image states:

**"An automobile dealership received six cars that needed to be detailed. If the service staff took \( 8 \frac{1}{4} \) hours to detail the automobiles, how long (in hours) did each car take?"**

### Solution:

To find how long each car took, you need to divide the total time taken by the number of cars.

1. **Convert mixed fraction to an improper fraction:**

   The total time is given as \( 8 \frac{1}{4} \) hours.
   \[
   8 \frac{1}{4} = \frac{8 \times 4 + 1}{4} = \frac{33}{4} \text{ hours}.
   \]

2. **Divide by the number of cars:**

   You need to divide the total time \( \frac{33}{4} \) hours by 6 cars.
   \[
   \text{Time per car} = \frac{\frac{33}{4}}{6} = \frac{33}{4} \times \frac{1}{6} = \frac{33}{24} = \frac{11}{8} \text{ hours}.
   \]

3. **Convert the result to a mixed fraction:**

   \[
   \frac{11}{8} = 1 \frac{3}{8} \text{ hours}.
   \]

Thus, each car took **\( 1 \frac{3}{8} \) hours** to be detailed.

Would you like any further details or clarifications on this? Here are a few related questions to deepen your understanding:

1. How do you divide fractions?
2. What is the general process for converting improper fractions into mixed fractions?
3. Can you explain how to multiply fractions?
4. How would the solution change if the service time were \( 9 \frac{1}{2} \) hours?
5. How could you estimate the time per car mentally without a calculator?

**Tip**: When dividing by whole numbers, you can multiply by the reciprocal (flip the fraction) to simplify your calculations!

An automobile dealership received six cars that needed to be detailed. If the service staff took 8 1/4 hours to detail the automobiles, how long (in hours) did each car take?

Learn how to calculate the time taken to detail each car when 6 cars are detailed in a total of 8 1/4 hours. This problem covers fraction division and mixed fraction conversion. Suitable for middle school students in Grades 6-8.

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