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?

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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:
{{{P/8 + P/x = P/6}}}

or (since P cancels out)
{{{1/8 + 1/x = 1/6}}}

Simplifying by multipling by 24*x throughout

{{{3*x + 24 = 4*x}}} or {{{x = 24}}}

So working alone, Vivian would take {{{highlight(24)}}} hours to paint the house.

Hope this helps!
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