If Andrew can do a job in 8 hours and Bobby can do the same job in 12 hours, how long would it take the two men working together in hours?

To solve this, we can use the concept of combined work rates. The work rates of Andrew and Bobby are their individual rates of completing the job per hour. Here's the breakdown:

- Andrew's rate is \( \frac{1}{8} \) of the job per hour.
- Bobby's rate is \( \frac{1}{12} \) of the job per hour.

When they work together, their rates add up:

\[
\text{Combined rate} = \frac{1}{8} + \frac{1}{12}
\]

To add these fractions, we need to find a common denominator. The least common denominator of 8 and 12 is 24. Converting both fractions:

\[
\frac{1}{8} = \frac{3}{24}, \quad \frac{1}{12} = \frac{2}{24}
\]

Now, add them together:

\[
\frac{3}{24} + \frac{2}{24} = \frac{5}{24}
\]

Thus, their combined rate is \( \frac{5}{24} \) of the job per hour. To find how long it would take them to complete the job together, we take the reciprocal of their combined rate:

\[
\text{Time} = \frac{1}{\frac{5}{24}} = \frac{24}{5} = 4.8 \text{ hours}
\]

So, it would take Andrew and Bobby approximately **4.8 hours** to complete the job together.

Would you like more details on this process or have any further questions?

Here are 5 related questions:
1. What if Andrew could do the job in 6 hours instead of 8? How would the time change?
2. How would you calculate the combined time if a third person, Charlie, could do the job in 10 hours?
3. Can you express the combined work rate as a percentage of the job done per hour?
4. How would the total time change if Andrew took breaks and only worked half the time?
5. What if Bobby worked twice as fast as he currently does? How would that affect the time?

**Tip**: When dealing with work problems, always think of rates in terms of jobs per hour—it simplifies the calculation process.

Learn how to calculate the time it takes for two people, Andrew and Bobby, to complete a job together. Andrew finishes the job in 8 hours, and Bobby in 12 hours. This problem covers key mathematical concepts such as work rates, adding fractions, and the reciprocal property. Suitable for students in Grades 7-9.

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