To calculate how long it will take for both A and B to finish a job together, we use the concept of work rates. The rate of work for each person is how much of the job they complete in one day.

• A can complete the job alone in 6 days, so A's work rate is $\frac{1}{6}$ of the job per day.
• B can complete the job alone in 3 days, so B's work rate is $\frac{1}{3}$ of the job per day.

When they work together, their combined work rate is the sum of their individual work rates:

$\text{Combined work rate} = \frac{1}{6} + \frac{1}{3}$

First, we need to add these fractions:

$\frac{1}{6} + \frac{1}{3} = \frac{1}{6} + \frac{2}{6} = \frac{3}{6} = \frac{1}{2}$

So, A and B together can complete $\frac{1}{2}$ of the job per day. This means they will finish the job in:

$\text{Time} = \frac{1}{\text{Combined work rate}} = \frac{1}{\frac{1}{2}} = 2 \text{ days}$

Thus, A and B working together will finish the job in 2 days.

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Would you like further clarification or details?

Here are 5 related questions you might find interesting:

1. What happens if A and B start working at different times?
2. How would the time change if A worked at 80% of their efficiency?
3. How do you calculate the combined work rate if one person takes a break?
4. How does this apply to three workers with different individual rates?
5. What if A's time increases by 2 days due to delays?

Tip: When combining rates, always remember to add the fractions, and don't forget to find a common denominator if needed.