Question 812216
How long does it take robert to mow the lawn by himself?
<pre>
Let x = the number of hours it takes Robert to mow the lawn by himself.

So Robert's mowing rate is 1 lawn per x hours or {{{1_lawn/x_hr}}} or {{{1/x}}}{{{lawn/hr}}}.
</pre>
When Gene works alone it takes him 3 hours longer than it takes robert when he works alone.
<pre>
Then the number of hours it takes Gene to mow the lawn by himself = x+3

So Gene's mowing rate is 1 lawn per x+3 hours or {{{1_lawn/x+3_hr}}} or {{{1/(x+3)}}}{{{lawn/hr}}}.
</pre>
Working together gene and robert can mow the lawn in 2 hours.
<pre>
So their combined working rate is 1 lawn per 2 hours or {{{1_lawn/2_hr}}} or {{{1/2}}}{{{lawn/hr}}}.

The equation comes from 

    {{{(matrix(3,1,"Robert's",mowing,rate))}}}{{{""+""}}}{{{(matrix(3,1,"Gene's",mowing,rate))}}} {{{""=""}}} {{{(matrix(4,1,Their,combined,mowing,rate))}}}

             {{{1/x}}}{{{""+""}}}{{{1/(x+3)}}} {{{""=""}}} {{{1/2}}}

Multiply through by LCD = 2x(x+3)

Answer: x = 3 hours. 

Edwin</pre>