Question 249470
if one painter can paint a house in 6 hours, and another painter paints a house in 9 hours. How long will it take them to paint the house working together
<pre><font size = 4 color = "indigo"><b>
Let x = the number of hours working together (what is asked for)

Make this chart:

                  No. of Houses      Rate        Time
first painter
second painter
------------------------------------------------------
both together

Fill in x for the time for both together to paint 1 house:

                  No. of Houses      Rate        Time
first painter
second painter
------------------------------------------------------
both together        1                            x
</pre></font></b>
>>...one painter can paint a house in 6 hours...<<
<pre><font size = 4 color = "indigo"><b>
So fill in 1 house and 6 hours for the first painter,
his no. of houses and his number of hours, respectively.

                  No. of Houses      Rate        Time
first painter         1                           6
second painter         
------------------------------------------------------
both together         1                           x
</pre></font></b>
>>...another painter paints a house in 9 hours...<<
<pre><font size = 4 color = "indigo"><b>
So fill in 1 house and 9 hours for the second painter,
his no. of houses and his number of hours, respectively.

                  No. of Houses      Rate        Time
first painter         1                           6
second painter        1                           9
------------------------------------------------------
both together         1                           x

Now fill in all three rates using the formula

{{{rate = (Number_of_houses)/(Time)}}}

                  No. of Houses      Rate        Time
first painter         1              1/6          6
second painter        1              1/9          9
------------------------------------------------------
both together         1              1/x          x

Now form the equation by using the fact that

First painter's rate + Second painter's rate = their rate together

                     {{{1/6 + 1/9 = 1/x}}}

Can you get a LCD of 18x and solve that equation for x?
If not post again asking how to.

Answer:  {{{18/5}}} hours or {{{3&3/5}}} hours or {{{3.6}}} hours or  
         {{{3}}} hours and {{{36}}} minutes. 

Edwin</pre>