you take 8 hours to finish painting a room. Your friend takes 4 hours to finish. How long does it take both of you to complete it?

Question

 This type of question is on our last test. The teacher explained it, but i didn't really get it. Any help?

Answer 1

you take 8 hours to finish painting a room

so in 1 hr work done by you= 1/8 of room

your friend takes 4 hours to finish

so in 1hr work done by your friend = 1/4 of room

 

Let x = number of hours it would take you and your friend  together to paint the room, then working together, in 1 hour they can paint 1/x of the room

 

1/8 + 1/4 = 1/x

lcm of denominator is 8x

 

(x+2x)=8

3x = 8

x = 8/3

x= 2.67 hr