Question

It takes Nate five hours to paint a wall, and it takes Jill seven hours to paint the same wall. About how many hours will it will take if Nate and Jill work together to paint the wall?

Answer 1

Let's use the relation:

$\mathsf{\dfrac{1}{x} = \dfrac{1}{5} + \dfrac{1}{7}}\\ \\ \\ \mathsf{\dfrac{1}{x} = \dfrac{7+5}{35}}\\ \\ \\ \mathsf{\dfrac{1}{x} = \dfrac{12}{35}}\\ \\ \\ \mathsf{x = \dfrac{35}{12}}\\ \\ \\ \boxed{\mathsf{x\approx 2.92 \ h}}$

It would take about 3 hours to complete the work.