Question

Sally can paint the office​ by herself in 5 hours. Lucy can do the same job in 4 hours. How long will it take them to do it working together?

Answer 1

2.22 hours

Step-by-step explanation:

If Sally can paint the office by herself in 5 hours, we can say that in one hour she paints 1/5 of the office.

On the other hand, Lucy paints the office in 4 hours, which means that, in 1 hour she paints 1/4 of the office.

Therefore, to know how much they would paint per hour working together, we are going to sum up the fractions they paint per hour:

`(1)/(5) +(1)/(4)=(4+5)/(20) =(9)/(20)`

Therefore, working together they will paint
`(9)/(20)`
`=0.45` of the office in one hour.

Now we can establish a rule of three: if they paint 0.45 of the office in 1 hour, how long (x) will it take them to paint 1.0 of the office?

`1- 0.45\\x-1`

And therefore
`x = (1)/(0.45)=2.22`

Therefore, it will take them 2.22 hours to paint the office working together.