Question 883383
Pedro can do a piece work in 4 days,
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So Pedro's rate is {{{matrix(1,2,1,job)/matrix(1,2,4,days)}}}{{{""=""}}}{{{matrix(1,2,1/4,job/(day))}}}
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while Alan can do a piece of work in 5 days,
<pre>
So Alan's rate is {{{matrix(1,2,1,job)/matrix(1,2,5,days)}}}{{{""=""}}}{{{matrix(1,2,1/5,job/(day))}}}
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In how many days can both finish the work, if they work together?
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Let that be x days.

So their combined rate is {{{matrix(1,2,1,job)/matrix(1,2,x,days)}}}{{{""=""}}}{{{matrix(1,2,1/x,job/(day))}}}

The equation comes from:

{{{(matrix(3,1,"Pedro's",work, rate))}}}{{{""+""}}}{{{(matrix(3,1,"Alan's",work,rate))}}} {{{""=""}}} {{{(matrix(4,1,their,combined,work, rate))}}}

{{{matrix(1,2,1/4,job/(day))}}}{{{""+""}}}{{{matrix(1,2,1/5,job/(day))}}} {{{""=""}}} {{{matrix(1,2,1/x,job/(day))}}}

{{{1/4}}}{{{""+""}}}{{{1/5}}} {{{""=""}}} {{{1/x}}}

Multiply through by LCD of 20x

5x + 4x = 20
     9x = 20
      x = {{{20/9}}} or {{{2&2/9}}} days

Edwin</pre>