Question

Dave can paint the office by himself in 4 hours. Working with an associate, he can paint the

office in 3 hours. How long would it take his associate to do it working alone?

Answer 1

It would take 12 hours for his associate to do the complete work alone.

Explanation:

Let 'x' be the hours taken by his associate working alone.

Given:

Time to paint the office by Dave is 4 hours.

Time to paint the office together is 3 hours.

Therefore, the part of work completed by Dave alone in 1 hour is
`(1)/(4)`

Part of work completed by an associate in 1 hour is
`(1)/(x)`

Now part of work completed by both in 1 hour is
`(1)/(3)`

Therefore,

`(1)/(4)+(1)/(x)=(1)/(3)\\\\(1)/(x)=(1)/(3)-(1)/(4)\\\\(1)/(x)=(4-3)/(12)\\\\(1)/(x)=(1)/(12)\\\\x=12\ h`

Therefore, it would take 12 hours for his associate to do the complete work alone.