Question

If Fran were to paint her living room alone, it would take 6 hours. Her sister Denise

could do the job in 8 hours. How long would it take them working together? If needed,
submit your answer as a fraction reduced to lowest terms.

Answer 1

It will take Fran and Denise
`3(3)/(7)` hours to paint the living room.

Explanation:

Given that:

Time taken by Fran to paint living house = 6 hours

Time taken by Denise = 8 hours

Let,

x be the time taken by both of them.

`(1)/(Fran's\ share)+(1)/(Denise's\ share)=(1)/(x)\\\\(1)/(6)+(1)/(8)=(1)/(x)\\\\(4+3)/(24)=(1)/(x)\\\\(7)/(24)=(1)/(x)\\\\x = (24)/(7)`

`x = 3(3)/(7)` hours

Hence,

It will take Fran and Denise
`3(3)/(7)` hours to paint the living room.