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?

To find out how long it will take Rachel and Carl to finish the job together, we can use the formula for combined work rates. The combined rate of two people working together is the sum of their individual rates.

1. **Rachel's rate of work**:  
   Rachel finishes the entire job in 5 hours, so her rate of work is:
   \[
   \text{Rachel's rate} = \frac{1 \text{ job}}{5 \text{ hours}} = \frac{1}{5}
   \]

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

3. **Combined rate of work**:  
   The combined rate of work when they work together is the sum of their individual rates:
   \[
   \text{Combined rate} = \frac{1}{5} + \frac{1}{8} = \frac{8}{40} + \frac{5}{40} = \frac{13}{40}
   \]

4. **Time to finish the job together**:  
   The time to complete the job together is the reciprocal of their combined rate:
   \[
   \text{Time together} = \frac{1}{\frac{13}{40}} = \frac{40}{13} \text{ hours}
   \]
   \[
   \text{Time together} \approx 3.08 \text{ hours}
   \]

Thus, Rachel and Carl will take approximately **3.08 hours** to finish the job together.

Do you want more details or have any questions?

Here are 5 related questions:
1. What if Rachel works faster and can finish the job in 3 hours?
2. How would the result change if Carl could finish the job in 6 hours instead of 8?
3. What if Rachel and Carl took breaks halfway through the task?
4. How do you find the time if there were three people working together?
5. How would the formula change if one person works part-time?

**Tip:** When working with combined rates, always sum the rates of each person, and then take the reciprocal of the result to find the total time.

Discover how to calculate the time it takes for Rachel and Carl to finish a job together. Rachel can complete the job in 5 hours and Carl in 8 hours. This detailed solution explains work rate formulas and shows that they will finish together in approximately 3.08 hours. Suitable for Grades 6-8.

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