SOLUTION: Painting can be done in 8 hours if Jefferson and Pasha work together. How long will it take Jefferson and Pasha painting separately if Jefferson can complete the painting in half t

Question 1198439: Painting can be done in 8 hours if Jefferson and Pasha work together. How long will it take Jefferson and Pasha painting separately if Jefferson can complete the painting in half the time it would take Pasha painting alone?
Found 2 solutions by ankor@dixie-net.com, greenestamps:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Painting can be done in 8 hours if Jefferson and Pasha work together.
How long will it take Jefferson and Pasha painting separately if Jefferson can complete the painting in half the time it would take Pasha painting alone?
:
Let t = time required by J to do the job alone
"Jefferson can complete the painting in half the time it would take Pasha painting alone?"
therefore
2t = time required by P to do the job
:
Write a shared work equation, each will do a fraction of the job.
The two fractions add up to 1

multiply equation by 2t, cancel the denominators
2(8) + 8 = 2t
16 + 8 = 2t
2t = 24
t = 24/2
t = 12 hrs, J working alone
then obviously,
2(12) = 24 hrs p working alone
:
You can substitute these two values in the shared work equation to confirm this

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The solution from the other tutor shows a typical formal algebraic solution.

If formal algebra is not required, the problem can be solved quickly using logical reasoning and simple mental arithmetic.

Jefferson can do the job in half the time as Pasha; that means he works twice as fast as Pasha.

That means that when they work together Jefferson does 2/3 of the job and Pasha does 1/3.

It takes the two of them together 8 hours to do the job; in those 8 hours Pasha does 1/3 of the job.

And that means it would take Pasha 3*8 = 24 hours to do the whole job alone.

ANSWER: 24 hours

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