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?

Question

asked Sep 18, 2019 169k views

1 Answer

Lyrically Wicked · Answer 1 · 2019-09-25T07:29:54+0000

Answer: Ruben can clean the house in 8.4 hours.

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

(1)/(6)

Work done by both is given by

(1)/(3.5)

According to question, we get that

$(1)/(6)+(1)/(x)=(1)/(3.5)\\\\(x+6)/(6x)=(1)/(3.5)\\\\3.5(x+6)=6x\\\\3.5x+21=6x\\\\21=6x-3.5x\\\\21=2.5x\\\\x=(21)/(2.5)\\\\x=8.4$

Hence, Ruben can clean the house in 8.4 hours.