Question 686438
>>Working together, Linda and Kathy can clean a beach house in 5.14 hours.<<
<pre>
So, their rate working together is 1 house per 5.14 hours or 
{{{(1house)/(5.14hours)}}} or {{{1/5.14}}}{{{house/hours}}}
</pre>
>>Had she done it alone it would have taken Linda 11 hours.<< 
<pre>
So, Linda's rate working alone is 1 house per 11 hours or 
{{{(1house)/(11hours)}}} or {{{1/11}}}{{{house/hours}}}
</pre> 
>>How long would it take Kathy to do it alone?<<
<pre>
Suppose it would take Kathy x hours to do it alone.

So, Kathy's rate working alone is 1 house per x hours or 
{{{(1house)/(x_hours)}}} or {{{1/x}}}{{{house/hours}}}

The equation comes from:

                    {{{(matrix(4,1,
                   "Linda's", 
                   rate,
                   working,
                   alone))+(matrix(4,1,
                   "Kathy's", 
                   rate,
                   working,
                   alone))=(matrix(5,1,
                   their, 
                   combined,
                   rate,
                   working,
                   together))}}} 


                            {{{1/11}}} + {{{1/x}}} = {{{1/5.14}}}
Eliminate the decimal by multiplying top and bottom of the last fraction
by 100
                            {{{1/11}}} + {{{1/x}}} = {{{100/514}}}

Multiply through by 5654x

                       514x + 5654 = 1100x
                              5654 = 586x
                               {{{5654/586}}} = x
                               {{{2827/293}}} = x
                       9.648464164 = x

Round off to hundredths 9.65 hours.

Edwin</pre>