Question 153648
Suppose Susan can paint the house alone in x hours.
So their rates are:
(think of the whole job as 1.)
Ann alone can do {{{1/15}}} of the whole job per hour.
Susan alone can do {{{1/x}}} of the whole job per hour.
In 6 hours Ann can do {{{6*(1/15)}}} of the whole job.
In 6 hours Susan can do {{{6*(1/x)}}} of the whole job.
As working jointly both of them can complete the job in 6 hours, we have
{{{6*(1/15)+6*(1/x)=1}}}
Solving for x, we have
{{{15x(6*(1/15)+6*(1/x))=1*15x}}}    (multiply both sides by 15x)
{{{15x*6*(1/15)+15x*6*(1/x)=1*15x}}}
{{{6x+90=15x}}}
{{{90=9x}}}
{{{90/9=x}}}
{{{10=x}}}
{{{x=10}}}
So it takes Susan 10 hours to paint the house alone