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To solve the problem where Rachel can finish a job in 5 hours and Carl can finish the same job in 8 hours, we can use the concept of rates of work.

### Step-by-Step Solution:

1. **Rachel's rate of work**: Rachel can finish the job in 5 hours, so her work rate is:
   \[
   \text{Rachel's rate} = \frac{1 \text{ job}}{5 \text{ hours}} = \frac{1}{5} \text{ jobs per hour}.
   \]

2. **Carl's rate of work**: Carl can finish the job in 8 hours, so his work rate is:
   \[
   \text{Carl's rate} = \frac{1 \text{ job}}{8 \text{ hours}} = \frac{1}{8} \text{ jobs per hour}.
   \]

3. **Combined work rate**: If they work together, their combined rate is the sum of their individual rates:
   \[
   \text{Combined rate} = \frac{1}{5} + \frac{1}{8}.
   \]

   To add these fractions, we need a common denominator:
   \[
   \text{Combined rate} = \frac{8}{40} + \frac{5}{40} = \frac{13}{40} \text{ jobs per hour}.
   \]

4. **Time to complete the job together**: The time to complete one job is the reciprocal of the combined rate:
   \[
   \text{Time} = \frac{1 \text{ job}}{\frac{13}{40} \text{ jobs per hour}} = \frac{40}{13} \text{ hours}.
   \]

   Simplifying:
   \[
   \frac{40}{13} \approx 3.08 \text{ hours}.
   \]

### Final Answer:
Rachel and Carl working together will take approximately **3.08 hours** to complete the job.

Would you like further details or have any questions?

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Here are 5 related questions for further practice:

1. If Rachel and Carl work together but Carl takes a break after 2 hours, how much longer will Rachel take to finish the job alone?
2. What if Carl could finish the job in 6 hours instead of 8 hours? How long would it take them together?
3. Suppose Rachel works twice as fast as Carl; how long will they take to finish the job together?
4. If Rachel had a machine that makes her twice as fast, how long would they take to finish the job together now?
5. What if there was a third worker who could finish the job in 4 hours? How long would it take for all three to complete the job together?

**Tip:** Always check units when working with rates, ensuring you properly combine and interpret the rates before solving.

Rachel can finish the job in 5 hours, while Carl can finish the same job in 8 hours. How long will it take them to finish the job together?

Learn how to calculate the time it takes two workers, Rachel and Carl, to finish a job together. Rachel can finish the job in 5 hours, while Carl can finish it in 8 hours. This problem involves rates of work and fraction addition. Suitable for students in Grades 6-8.

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