Question

It takes nate four hours to paint a wall and it takes jill seven hours to paint the same wall about how many hours will it take if nate and jill work together to paint the wall

Answer 1

If Nate paints the wall in 4 hours, it means that he can paint 1/4 of the wall every hour.

Similarly, if Jill paints the wall in 7 hours, it means that he can paint 1/7 of the wall in one hour.

So, together, they paint the following fraction of the wall in one hour:

$\frac{1}{4}+\frac{1}{7} = \frac{4+7}{28} = \frac{11}{28}$.

At this rate, they need 28/11 hours to paint the whole wall, in fact, after that amount of time they paint

$\frac{11}{28}\frac{28}{11} = 1$

i.e. the whole wall