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Question 1184891: Nana can paint a room in 6 hours,Harith can do the job in 4 hours,but Angela need 2 hours to paint the same room.How long does it take them to paint the room if they work together?
Answer by greenestamps(13198)   (Show Source):
You can put this solution on YOUR website!
A standard algebraic solution....
Nana paints 1/6 of the room in 1 hour; Harith paints 1/4 of it in 1 hour; Angela paints 1/2 of it in 1 hour. So together in 1 hour the fraction of the room they paint is
1/6+1/4+1/2 = 2/12+3/12+6/12 = 11/12
So the number of hours it takes the three of them together to paint the room is 1/(11/12) = 12/11.
ANSWER: 12/11 hours
An alternative solution avoiding fractions....
The least common multiple of the three times is 12 hours.
In 12 hours, Nana could paint 12/6=2 of the rooms
In 12 hours, Harith could paint 12/4=3 of the rooms
In 12 hours, Angela could paint 12/2=6 of the rooms
So in 12 hours the three of them together could paint 2+3+6=11 of the rooms
So the number of hours it would take them to paint the one room is 12/11.
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