Question

Reynaldo can clean the house in 6 hours by himself. When Reynaldo and Ruben work together, it takes 3.5 hours. How long would it take Ruben to clean the house by himself?

Answer 1

Answer: Ruben can clean the house in 8.4 hours.

Step-by-step explanation:

Since we have given that

Number of hours Reynaldo can clean = 6 hours

Number of hours Reynaldo and Ruben can clean = 3.5 hours

Let the number of hours Ruben can clean be 'x'.

Work done by Reynaldo is given by

$\dfrac{1}{6}$

Work done by both is given by

$\dfrac{1}{3.5}$

According to question, we get that

$\dfrac{1}{6}+\dfrac{1}{x}=\dfrac{1}{3.5}\\\\\dfrac{x+6}{6x}=\dfrac{1}{3.5}\\\\3.5(x+6)=6x\\\\3.5x+21=6x\\\\21=6x-3.5x\\\\21=2.5x\\\\x=\dfrac{21}{2.5}\\\\x=8.4$

Hence, Ruben can clean the house in 8.4 hours.