Question

Maria can clean the entire house in two hours. Her sister, Sasha, can clean the house in three hours. How long would it take for two of them to do the job together?

Answer 1

72 minutes

We require their hourly rate of work

Maria cleans $\frac{1}{2}$ the house in 1 hour

Sasha cleans $\frac{1}{3}$ of the house in 1 hour

let x be the time it takes both to clean the house

$\frac{1}{2}$ + $\frac{1}{3}$ = $\frac{1}{x}$

multiply through by 6x

3x + 2x = 6

5x = 6 ⇒ x = $\frac{6}{5}$

Together they can clean the house in 72 minutes