A can complete `(2)/(3)` of work in 6 days. In what time can he complete `(4)/(9)` of the work ?

Answer

To solve the problem step by step, we will first determine how much work A can complete in one day and then use that information to find out how long it will take to complete \( \frac{4}{9} \) of the work.

### Step 1: Determine the total work done by A
A can complete \( \frac{2}{3} \) of the work in 6 days. Therefore, the total work can be represented as:

\[ \text{Total Work} = \frac{2}{3} \text{ work in 6 days} \]

### Step 2: Calculate the work done in one day
To find out how much work A does in one day, we can divide the work done by the number of days:

\[ \text{Work done in one day} = \frac{\frac{2}{3}}{6} = \frac{2}{3} \times \frac{1}{6} = \frac{2}{18} = \frac{1}{9} \]

So, A can complete \( \frac{1}{9} \) of the work in one day.

### Step 3: Determine how long it takes to complete 1 unit of work
Since A completes \( \frac{1}{9} \) of the work in one day, to complete 1 unit of work, we can find the number of days required:

\[ \text{Days to complete 1 unit} = \frac{1}{\frac{1}{9}} = 9 \text{ days} \]

### Step 4: Calculate the time to complete \( \frac{4}{9} \) of the work
Now, we need to find out how long it will take A to complete \( \frac{4}{9} \) of the work. Since A takes 9 days to complete 1 unit of work, we can calculate the time for \( \frac{4}{9} \) of the work as follows:

\[ \text{Time for } \frac{4}{9} \text{ of the work} = 9 \times \frac{4}{9} = 4 \text{ days} \]

### Final Answer
A can complete \( \frac{4}{9} \) of the work in **4 days**.

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