A do work in 10 days and B do same work in 8 days find in how many days both AandB together do that work

To find out how many days it takes for both A and B to complete the work together, we can use the concept of work rates. Here’s how it can be done:

1. Let’s denote the total work as \( W \).

2. A can complete the work in 10 days. So, A’s work rate is \( \frac{W}{10} \) per day.

3. B can complete the work in 8 days. So, B’s work rate is \( \frac{W}{8} \) per day.

4. When A and B work together, their combined work rate is the sum of their individual work rates:
   \[
   \text{Combined work rate} = \frac{W}{10} + \frac{W}{8}
   \]

5. To add these fractions, we need a common denominator. The least common multiple of 10 and 8 is 40. So,
   \[
   \frac{W}{10} = \frac{4W}{40} \quad \text{and} \quad \frac{W}{8} = \frac{5W}{40}
   \]

6. Adding these fractions gives:
   \[
   \frac{4W}{40} + \frac{5W}{40} = \frac{9W}{40}
   \]

7. The combined work rate of A and B is \( \frac{9W}{40} \) per day. Therefore, the number of days it takes for A and B to complete the work together is:
   \[
   \text{Time} = \frac{W}{\frac{9W}{40}} = \frac{40}{9} \text{ days}
   \]

So, A and B together can complete the work in \( \frac{40}{9} \approx 4.44 \) days.

Would you like a detailed breakdown or have any questions? Here are some other questions you might be interested in:

1. How to solve quadratic equations?
2. How to find the derivative of a function?
3. What is the Pythagorean theorem?
4. How to integrate a function?
5. What are the properties of logarithms?

**Tip:** When dealing with work rate problems, always convert the individual rates into a common unit before combining them.

Understand how to calculate the combined work rate of A and B and determine how long it takes for them to complete a task together. This problem involves work rates and fraction addition, suitable for students in Grades 7-9.

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