Question

`A` takes 6 days less than the time taken by `B` to finish a piece of work. If both `A` and `B` together can finish it in 4 days, how many days will `B` take to finish the work?

Answer 1

We call the time it takes for B to finish the piece of work `x`.

For problems like these, we must consider how much work can be done in one day.

`1/x + 1/(x- 6) = 1/4`

`(x - 6)/(x(x - 6)) + x/(x(x - 6)) = 1/4`

`4(x - 6 + x) = x^2 - 6x`

`4(2x- 6) = x^2 - 6x`

`8x - 24 = x^2 - 6x`

`0 = x^2 - 14x + 24`

`0 = (x- 12)(x - 2)`

`x = 12 and 2`

If the time it takes `B` is `2` days, then the time it takes `A` is `-4` days, which has no sense.

Therefore, it would take `B` a period of `12` days to finish the job.

Hopefully this helps!