Answer:

Step-by-step explanation:

A takes 9 days more than B to do a certain piece of work. Together they can do the work

in 6 days. How many days will A alone take to do the work ?

Let's denote the time B takes to do the work as

�

B days. According to the given information:

�

A takes 9 days more than

�

B to do the work, so the time

�

A takes is

�

+

9

B+9 days.

Together, they can do the work in 6 days.

The combined rate of

�

A and

�

B is the sum of their individual rates. The rate is inversely proportional to the time taken. So, if

�

A takes

�

A days to complete the work, then the rate of

�

A is

1

�

A

1

​

 and the rate of

�

B is

1

�

B

1

​

.

The combined rate is then

1

�

+

1

�

A

1

​

+

B

1

​

, and it's given that together they can complete the work in 6 days. Therefore, we can write the equation:

1

�

+

1

�

=

1

6

A

1

​

+

B

1

​

=

6

1

​

Now, we know that

�

=

�

+

9

A=B+9. We can substitute this into the equation:

1

�

+

9

+

1

�

=

1

6

B+9

1

​

+

B

1

​

=

6

1

​

To solve this equation and find the values of

�

A and

�

B, you can multiply through by the common denominator and then solve for

�

B. Once you find

�

B, you can then find

�

A since

�

=

�

+

9

A=B+9.

Please note that the solution involves algebraic manipulation, and the final answer will provide the number of days

�

A alone takes to do the work.

Let's denote the amount of work that A can do in one day as `1/A` and the amount of work that B can do in one day as `1/B`.

According to the problem, A takes 9 days more than B to do the work, so we can write this as `A = B + 9`.

Also, A and B together can do the work in 6 days, which means `(1/A) + (1/B) = 1/6`.

Substituting `A = B + 9` into the second equation, we get `(1/(B+9)) + (1/B) = 1/6`.

Solving this equation for B, we get `B = 7.5`.

Substituting `B = 7.5` into `A = B + 9`, we get `A = 16.5`.

So, A alone will take 16.5 days to do the work.