<PRE><B>Question 78254</B>
A painter works on a job for 10 days and then is joined by a helper. Together they finish the job in 6 more days. The helper could have done the job alone in 30 days. How long would have taken the painter have taken to do the job alone.
:
Let x = number of days that the painter can do the job by himself
:
Let the completed job = 1
Painter alone + Painter/Helper = 1
:
{{{10/x}}} + {{{6/x}}} + {{{6/30}}} = 1
:
Multiply equation by 30x, gets rid of the denominators:
30(10) + 30(6) + 6x = 30x
:
300 + 180 = 30x - 6x
:
24x = 480
x = 480/24
x = 20 days, the painter by himself
:
:
Check: 
10/20 + 6/20 + 6/30 =
 5/10 + 3/10 + 2/10 = 1</PRE>