Question

After painting the fence steve and janet realize that their house also needs painting. But steve will have to do the painting himself since janet has injured her shoulder. Before getting started, steve wants to find out how long the project will take. He determines that it would take them 9 days to paint the house together (if they were both healthy) and that it would take janet (when healthy) 16 days to paint the house alone. How long will it take steve to paint the house alone?

Answer 1

Therefore, Steve will paint house for 20.6 days.

Explanation:

We know that Steve determines that it would take them 9 days to paint the house together (if they were both healthy) and that it would take Janet (when healthy) 16 days to paint the house alone.

We conclude that in 1 day Janet painted 1/16 of the house. In nine days, Janet painted 9/16 of house.

So, 7/16 of house paint Steve in nine days.

We have the following proportion:

`(7)/(16):9=1:x\\\\(7)/(16)x=9\\\\x=9\cdot (16)/(7)\\\\x=20.6`

Therefore, Steve will paint house for 20.6 days.