Question

Elias and Niko are polishing the silver at the heritage museum.Elias could polish all the silver himself in 40 minutes.That task would take Niko 50 minutes to complete alone.Whick table is filled in correctly and could be used to determine how long it would take Elias and Niko polished te silver together?

Answer 1

Let x be the time it takes Elias and Niko to polish the silver working together. If Elias works alone, he could polish all the silver himself in 40 minutes. Then, in 1 minute, he will make $\frac{1}{40}$ of the total work. If the same analysis is applied Niko, in 1 minute, will make $\frac{1}{50}$ of the total work.

Working together Elias and Niko will need x minutes to make all the work. Then, in 1 minute, they will make $\frac{1}{x}$ of the total work.  So, the fraction of the total work they make in 1 minute is given by this equation:

$\frac{1}{x}=\frac{1}{40}+\frac{1}{50} \\ \\ \frac{1}{x}=\frac{50+40}{2000} \\ \\ x=\frac{2000}{90} \\ \\ \boxed{x=22.22 minutes}$

Answer 2

We let x be the number of hours both could the job together.
The fraction of the job done by Elias is
x/40

The fraction of the job done by Niko is
x/50

Together they would be able to finish the job (one job)

x/40 + x/50 = 1
x = 1 / (1/40 + 1/50)
x = 22.22 minutes