Question 1026725
<pre>
Alfred's rate is 1 house per x days or 1/x house per day.
Bill's rate is 1 house per y days or 1/y house per day.
</pre>
If Alfred can only do 2/3 as much work as Bill
<pre>
So 1/x = (2/3)(1/y)

or 1/x = 2/(3y)
</pre>
Alfred and Bill working together can paint a house in 24 days. 
<pre>
Their combined rate is 1/x + 1/y house per day.

their combined rate times 24 days = 1 house painted. So

(24)(1/x+1/y) = 1 house painted

So we have the system of equations:

{{{system(1/x = (2/3)(1/y),(24)(1/x+1/y) = 1)}}}

Simplifying

{{{system(1/x = 2/(3y),1/x+1/y = 1/24)}}}


Substitute 2/(3y) for 1/x in the second equation:

{{{2/(3y)+1/y) = 1/24)}}}

{{{2/(3y)+3/(3y) = 1/24)}}}

{{{5/(3y) = 1/24)}}}

{{{3y=24*5}}}

Divide both sides by 3

{{{y=8*5}}}

{{{y=40}}}

Substitute in 

{{{1/x+1/y = 1/24}}}

{{{1/x+1/40 = 1/24}}}

Multiply through by LCD = 120

{{{120+3x = 5x}}}

{{{120=2x}}}

{{{60=x}}}

Edwin</pre>