Question

Carlos can paint a certain fence in 3 hours. If Magno helps him, the job takes only 2 hours to finish. How long would it take Magno to paint the fence by himself?

Answer 1

Magno would take `6` hours on his own.

Explanation:

We would expect that if there were two people painting it would take them half as long, which would be `3 "hours " div2 =1 1/2` hours.
But it takes them `2` hours which tells us that Magno paints at a slower rate than Carlos.

On his own, Carlos takes `3` hours for the whole job, which means that he does `1/3` of the job every hour. `1/3+1/3+1/3 = 1`

So after `2` hours Carlos has done `2/3` of the job, while Magno has done only `1/3` of the job in the `2` hours.

In one hour Magno would have done `1/3 div 2 =1/6`of the work, so if he were to paint on his own it would take him `6` hours to complete.

`1 div 1/6 = 6` hours