Question 1078031
Notice that the preceding answer 1.5 hrs, could not be correct because
Jim alone could paint the door in 1 hour.  Surely Kim couldn't slow
Jim down that much.  LOL

</pre>
Kim can paint the garage door in 2 hours and Jim can paint the same door in 1 hour. How long will it take them if they work together?
<pre>
You can do it with or without algebra.

Without algebra, just basic math:

If both work together for 2 hours painting garage doors
(say in a new development of houses), Kim will paint
1 garage door while Jim, the faster will paint 2 garage
doors, so together they can paint 3 garage doors in 2 
hours. So they can paint 1 garage door in 1/3 of 2 hours
which is 1/3 of 120 minutes or 40 minutes.

With algebra:
</pre>
How long will it take them if they work together?
<pre>Let the answer be x hours.
</pre>
Kim can paint the garage door in 2 hours.
<pre>
So Kim's painting rate is 1 door per 2 hours or {{{matrix(1,2,1,door)/matrix(1,2,2,hours)}}} or {{{matrix(1,2,1/2,door/hour)}}}
</pre>
Jim can paint the same door in 1 hour
<pre>
So Kim's painting rate is 1 door per 1 hour or {{{matrix(1,2,1,door)/matrix(1,2,1,hour)}}} or {{{matrix(1,2,1,door/hour)}}}

Together they can paint the same door in x hours:

So together their combined painting rate is 1 door per x hours or {{{matrix(1,2,1,door)/matrix(1,2,x,hours)}}} or {{{matrix(1,2,1/x,door/hour)}}}

The equation comes from:

{{{matrix(1,7,

(matrix(3,1,"Kim's",painting,rate)),
""+"",

(matrix(3,1,"Jim's",painting,rate)),
"",
""="",
"",

(matrix(4,1,Their,combined,painting,rate)))}}}

 {{{matrix(1,7,

matrix(1,2,1/2,door/hour),
""+"",
matrix(1,2,1,door/hour),
"",
""="",
"",
matrix(1,2,1/x,door/hour))}}}

{{{1/2+1}}}{{{""=""}}}{{{1/x}}}

Multiply through by 2x

{{{x+2x}}}{{{""=""}}}{{{2}}}

{{{3x}}}{{{""=""}}}{{{2}}}

{{{x}}}{{{""=""}}}{{{2/3}}}

2/3 of an hour is 2/3 of 60 minutes = 40 minutes.

Edwin</pre>