A takes 6 days less than B to do a work. If both A and B working together can do it in 4 days how many days will B take to finish it?

Question

Philoid · Accepted Answer

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.

Work done by B in 1 day = 1/x

Work done by A in 1 day = 1/(x – 6)

4(2x – 6) = x(x – 6)

8x – 24 = x² – 6x

x² – 14x + 24 = 0

(x – 12)(x – 2) = 0

⇒ x = 12 or x = 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.