SOLUTION: I know there is alot of similar questions, but I couldn't find the answer to this challenge offered by my teacher.. Nick can paint a fence by himself in 6 hours. When he works w

Question 976086: I know there is alot of similar questions, but I couldn't find the answer to this challenge offered by my teacher..
Nick can paint a fence by himself in 6 hours. When he works with his brother James they can paint a fence in 4 hours. How long would it take James to paint a fence by himself?
Found 2 solutions by FrankM, Alan3354:
Answer by FrankM(1040) (Show Source): You can put this solution on YOUR website!
In a day (24 hours) Nick paints 4 fences.
In a day James and Nick paint 6 fences.
Nick still paints 4 fences in a day, so James painted 2. James takes 12 hours per fence.

The above is a fool proof method to solve this problem, but it lacks the algebra type of set up the teacher might like.
Nick's rate is 1/6 fence per hour. This is key, as hours per fence will not work.
Nick + James' combined rate is 1/4 fence per hour.
1/6 + X = 1/4
4/24 + X = 6/24
X = 2/24, i.e. James' rate is 1 fence per 12 hours.
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Nick can paint a fence by himself in 6 hours. When he works with his brother James they can paint a fence in 4 hours. How long would it take James to paint a fence by himself?
-----------------
Nick paints 1/6 of a fence per hour.
James takes J hours --> he paints 1/J of a fence per hour.
----
Together, they paint 1/6 + 1/J per hour = 1/4 per hour
1/6 + 1/J = 1/4
(J + 6)/6J = 1/4
J + 6 = 6J/4
6J = 4J + 24
2J = 24
J = 12 hours

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