Question 673715
George can do a work in 60 days. 
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So George's rate is 1 job per 60 days or {{{("1_job(s)")/("60_day(s)")}}} = {{{1/60}}}job(s)/day(s)

Let Paul do 1 job in x days, then Paul's rate is 1 job per x days or {{{("1_job(s)")/("x_day(s)")}}} = {{{1/x}}}job(s)/day(s) 
</pre>
George and Paul can do the same work in 20 days.
<pre>
So together they can do 1 job in 20 days, so their combined rate is 
1 job per 20 days or {{{("1_job(s)")/("20_day(s)")}}} = {{{1/20}}}job(s)/day(s)

The equation comes from:

            {{{(matrix(4,1,

"George's", rate, in, "job(s)/day(s)"))}}} + {{{(matrix(4,1,

"Paul's", rate, in, "job(s)/day(s)"))}}} = {{{(matrix(5,1,

their, combined, rate, in, "job(s)/day(s)"))}}} 

             {{{1/60}}} + {{{1/x}}} = {{{1/20}}}

Multiply through by LCD of 60x

             x + 60 = 3x

                -2x = -60

                  x = 30

So Paul will take 30 days to complete the same work if he works alone.

Edwin</pre>