Question

A can do a piece of work in x days and B can do it in (x – 6) days. If working together, they can do it in 4 days, find the value of x.

Answer 1

Let A do the work in x days and B do it in (x − 6) days.

Write their one-day work

A’s one-day work = `1/x`

B’s one-day work = `1/(x-6)`

Working together, they complete the work in 4 days, so:

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

`= 1/4`

Take LCM x(x − 6):

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

`(2x -6)/(x(x-6)) = 1/4`

Cross-multiply:

4(2x − 6) = x(x − 6)

8x − 24 = x² − 6x

x² − 14x + 24 = 0

(x − 12) (x − 2) = 0

x = 12 or x = 2

x = 2 since x − 6 would be negative.

x = 12

So, A can do the work in 12 days and B in 6 days.