SOLUTION: Tom and Vivian are painting their house. If Tome were to work alone, it would take him 8 hours to paint the house. Together, Tome and Vivian can paint the house in 6 hours. How lon
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-> SOLUTION: Tom and Vivian are painting their house. If Tome were to work alone, it would take him 8 hours to paint the house. Together, Tome and Vivian can paint the house in 6 hours. How lon
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Question 966358: Tom and Vivian are painting their house. If Tome were to work alone, it would take him 8 hours to paint the house. Together, Tome and Vivian can paint the house in 6 hours. How long would it take Vivian to paint the house alone?
Thank you for answering! Found 2 solutions by amarjeeth123, ramkikk66:Answer by amarjeeth123(570) (Show Source):
You can put this solution on YOUR website! If Tome were to work alone, it would take him 8 hours to paint the house.
In 1 hour he can paint 1/8th of the house.
Together, Tome and Vivian can paint the house in 6 hours.
In 1 hour they can paint 1/6th of the house.
In 1 hour Vivian can paint (1/6-1/8)=(4-3)/24=1/24th of the house.
Vivian can paint the house in 24 hours.
You can put this solution on YOUR website! Tom and Vivian are painting their house. If Tome were to work alone, it would take him 8 hours to paint the house. Together, Tome and Vivian can paint the house in 6 hours. How long would it take Vivian to paint the house alone?
Let the total effort required to paint be P.
Tom does P/8 work in an hour
Let Vivian take x hours to paint alone.
So in one hour, Vivian does P/x of the work
Working together, in one hour they do P/6 of the work (since they complete P in 6 hours)
Which gives the equation:
or (since P cancels out)
Simplifying by multipling by 24*x throughout
or
So working alone, Vivian would take hours to paint the house.
Hope this helps!
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