SOLUTION: Tom and Jack paint a house. Working together they can paint the house in 2/3 of the time it takes Tom. Jack takes 6 hours to paint alone. How long does it take Tom to paint alone

Question 226895: Tom and Jack paint a house. Working together they can paint the house in 2/3 of the time it takes Tom. Jack takes 6 hours to paint alone. How long does it take Tom to paint alone>?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Tom and Jack paint a house.
Working together they can paint the house in 2/3 of the time it takes Tom.
Jack takes 6 hours to paint alone. How long does it take Tom to paint alone>?
:
Let t = time taken by Tom alone
then
t = time working together
:
Let the completed job = 1
:
The shared work equation:
+ = 1
Cancel t, and 2 into 6;
+ = 1
Multiply equation by 3, results
2 + = 3
:
Multiply equation by 3 again
3(2) + t = 3(3)
6 + t = 9
t = 9 - 6
t = 3 hrs is Tom's time alone
:
:
Check solution:
(2/3)*3 = 2 hrs working together
+ = 1

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