Question

Blake and Ned work for a home remodeling business. They are putting the final touches on a home they renovated. Working alone, Blake can paint one room in 9 hours. Ned can paint the same room in 6 hours. How long will it take them to paint the room if they work together?

Answer 1

Blake can do the work in 9 and part of work in 1 hour = 1/9

Ned can paint the same room in six hours, as well as do part of work in 1 hour = 1/6

If they do it together = 1/9+1/6=5/118, and they can do 5/18 part of work in hour = 1

So, they can do whole work in hours = 1/5/18=3.6

So if they do it together it will only take 3.6 hours.

Answer 2

Answer: The time taken by both of them if they work together is given by

`3(3)/(5)\ hours`

Explanation:

Since we have given that

Time taken by Blake to paint one room = 9 hours

Time taken by Ned to paint one room = 6 hours

Work done by Blake =
`(1)/(9)`

Work done by Ned =
`(1)/(6)`

Total work done by both of them together is given by

`(1)/(6)+(1)/(6)\\\\=(3+2)/(18)\\\\=(5)/(18)`

So, the time taken by both of them if they work together is given by

`(18)/(5)=3(3)/(5)\ hours`