Q:

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? (SHOW WORK)

Accepted Solution

A:
Answer: The time taken by both of them if they work together is given by[tex]3\dfrac{3}{5}\ hours[/tex]Step-by-step explanation:Since we have given that Time taken by Blake to paint one room = 9 hoursTime taken by Ned to paint one room = 6 hoursWork done by Blake Β = [tex]\dfrac{1}{9}[/tex]Work done by Ned = [tex]\dfrac{1}{6}[/tex]Total work done by both of them together is given by[tex]\dfrac{1}{6}+\dfrac{1}{6}\\\\=\dfrac{3+2}{18}\\\\=\dfrac{5}{18}[/tex]So, the time taken by both of them if they work together is given by[tex]\dfrac{18}{5}=3\dfrac{3}{5}\ hours[/tex]