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

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

$3\dfrac{3}{5}\ hours$

Step-by-step 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  = $\dfrac{1}{9}$

Work done by Ned = $\dfrac{1}{6}$

Total work done by both of them together is given by

$\dfrac{1}{6}+\dfrac{1}{6}\\\\=\dfrac{3+2}{18}\\\\=\dfrac{5}{18}$

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

$\dfrac{18}{5}=3\dfrac{3}{5}\ hours$

Answer 2

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.