How long will it take a and b to finish the job that can be done by a alone is 6 fays and b alone in 3 days

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.

How long will it take for A and B to finish the job if A alone can do it in 6 days and B alone in 3 days?

Find out how to calculate the time it takes for two workers, A and B, to finish a job together. Given that A can do the job alone in 6 days and B alone in 3 days, learn how to use work rates and fractions to solve this problem step-by-step. Suitable for students in Grades 6-8.

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