Question 994052
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Two painters, working together, can paint a house in 3 days.
One painter working alone can paint the house in 4 days.
How many days would it take the second painter, working alone,to paint the house.
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Let  {{{x}}}  be the number of days for the second painter to paint the house,  working alone.

Then the second painter paints  {{{1/x}}}  of the house per day.  It is his rate of work.


The first  painter can paint  {{{1/4}}}  of the house per day.  It is his rate of work.


Working together, they paint {{{1/3}}} of the house per day.


It gives an equation


{{{1/4}}} + {{{1/x}}} = {{{1/3}}}.


Simplify and solve it.  Multiply both sides by  12x  (it is the common denominator).  You will get


3x + 12 = 4x.


Hence, x = 12.


<U>Answer</U>. &nbsp;The second painter can paint the house in &nbsp;15&nbsp; days.


For more problems on joint work see the lesson &nbsp;<A HREF=http://www.algebra.com/algebra/homework/Rate-of-work-word-problems/Word-problems-WORKING-TOGETHER-by-Fractions.lesson>Using fractions to solve word problems on joint work</A>&nbsp; in this site.