Question

A and B working together can do a work in 6 days. If A takes 5 days less than B to finish the work, in how many days B alone can do the work.

Answer 1

15 days

Explanation:

Let x be the number of days needed for B to complete the job. Then x-5 is the number of days needed for A to complete the job.

In 1 day,

• A completes
  `(1)/(x-5)` of all work;
• B completes
  `(1)/(x)` of all work.

Hence, in 1 day both A and B complete
`(1)/(x-5)+(1)/(x)` of all work. A and B working together can do a work in 6 days. Then

`6\cdot \left((1)/(x-5)+(1)/(x)\right)=1.`

Solve this equation:

`(6x+6x-30)/(x(x-5))=1,\\ \\12x-30=x^2-5x,\\ \\x^2-17x+30=0,\\ \\D=(-17)^2-4\cdot 30=289-120=169=13^2,\\ \\x_(1,2)=(17\pm 13)/(2)=2,\ 15.`

If
`x=2,` then
`x-5=-3` that is impossible. So, B needs 15 days to complete the work alone.