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Question 694392: If a painter can paint a house in 6 hours and his apprentice can paint the same sized house in 9 hours, how long will it take for them to paint a house if they worked together?"
Found 3 solutions by jim_thompson5910, checkley79, ptaylor:
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! 1/6 + 1/9 = 1/t
3/18 + 2/18 = 1/t
5/18 = 1/t
5t = 18
t = 18/5
So it will take them 18/5 hours, or 3 and 3/5 hours (or 3.6 hours = 3 hours and 36 minutes) if they work together.
Answer by checkley79(3341) (Show Source):
Answer by ptaylor(2198)  (Show Source):
You can put this solution on YOUR website! Let x=amount of time it takes both working together to paint the house
So, working together, they paint at the rate of 1/x house per hour
The painter paints at the rate of 1/6 house per hour
The apprentice paints at the rate of 1/9 house per hour
So, working together, they paint at the rate of 1/6 + 1/9 =3/18 +2/18=5/18 house per hour
Our equation to solve, then, is:
5/18=1/x multiply each side by 18x or cross-multiply
5x=18
x=18/5 hours=3 3/5 hours---time it takes both working together
CK
In 18/5 hours, the painter paints (18/5)(1/6)=3/5 of the house
In 18/5 hours the apprentice paints (18/5)(1/9) =2/5 of the house
3/5 + 2/5 =5/5 which is all of the house :)
Hope this helps----ptaylor
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