Question 727936
the larger of two printers being used to print the payroll for a major corporation requres 40 min. to print the payroll. 
<pre>
So the larger printer's payroll printing rate is 

1 payroll per 40 min or {{{1_payroll/40_min}}} or {{{1/40}}}{{{payroll/min}}}
</pre>
>>...How long would it take the smaller printer working alone to print the payroll?...<<
<pre>
Let the answer be x min

So the smaller printer's payroll printing rate is 

1 payroll per x min or {{{1_payroll/x_min}}} or {{{1/x}}}{{{payroll/min}}}
<pre>
>>...After both printers have been operating for 10 min, the larger printer malfunctions...<<
<pre>
So the fraction of the payroll that the larger printer did in the 10 minutes
is {{{10_min*expr(1/40)}}}{{{payroll/min}}} = {{{1/4}}}payroll.
</pre>
>>... The smaller printer requires 50 more min to complete the payroll...<<
<pre>
The smaller printer printed the entire 60 minutes.

So the fraction of the payroll that the smaller printer did in the whole 60
minutes is {{{60_min*expr(1/x)}}}{{{payroll/min}}} = {{{60/x}}}payroll.
 
Together they printed 1 payroll:

       {{{(matrix(13,1,

PART,OF,PAYROLL,THE,LARGER,PRINTER,DID,IN,THE,10,MINUTES,IT,WORKED))}}}{{{""+""}}}{{{(matrix(14,1,

PART,OF,PAYROLL,THE,SMALLER,PRINTER,DID,IN,THE,ENTIRE,60,MINUTES,IT,WORKED))}}}{{{""=""}}}{{{(matrix(3,1, ONE,COMPLETE,PAYROLL))}}}

             {{{1/4}}}{{{""+""}}}{{{60/x}}}{{{""=""}}}{{{1}}}

Multiply through by LCD of 4x

              x + 240 = 4x
                  240 = 3x
                   80 = x

It would take the smaller printer 80 minutes to print the entire payroll. 
   
Edwin</pre>