Question 479833
<pre>
Let n be the number of machines of each type that were used to
complete the job in only 2 hours.

Make this chart.  (After you get the hang of how to do these
problems you may not need to do a chart, but make one anyway
to get the hang of it):

                             jobs     hrs.     rate in
                             done   required   jobs/hr
1 type R machine alone         
1 type S machine alone        
n type R machines together    
n type S machines together     
n type R's and n type S's      

In each case 1 job was done, so fill in 1 for the jobs done in
all 5 cases:


                             jobs     hrs.     rate in
                             done   required   jobs/hr
1 type R machine alone         1       
1 type S machine alone         1       
n type R machines together     1                
n type S machines together     1                
n type R's and n type S's      1       

We are told the no. of hours required in 3 of the cases.
We fill those in

                             jobs     hrs.     rate in
                             done   required   jobs/hr
1 type R machine alone         1       36       
1 type S machine alone         1       18       
n type R machines together     1                
n type S machines together     1                
n type R's and n type S's      1        2        

Now we can fill in the rates in job/hr by dividing jobs by hours:


                             jobs     hrs.     rate in
                             done   required   jobs/hr
1 type R machine alone         1       36       1/36
1 type S machine alone         1       18       1/18
n type R machines together     1                
n type S machines together     1                
n type R's and n type S's      1        2        1/2

since 1 type R machine's rate is 1/36 jobs/hr, n type R machines
would have a rate n times as fast or n/36 jobs/hr.  Similarly, n 
type S machines would have a rate of n times as fast as 1/18 or 
n/18 jobs/hr.   Fill those in:  

                             jobs     hrs.     rate in
                             done   required   jobs/hr
1 type R machine alone         1       36       1/36
1 type S machine alone         1       18       1/18
n type R machines together     1                n/36
n type S machines together     1                n/18
n type R's and n type S's      1        2        1/2

The equation comes from:

{{{(matrix(6,1,

rate,
of,
n,
type,
R,
machines))+
(matrix(6,1,

rate,
of,
n,
type,
S,
machines))=(matrix(8,1,

rate,
of,
n,
each,
of,
both,
type,
machines))}}}


{{{n/36 + n/18 = 1/2}}}

Multiply through by LCD = 36

{{{n + 2n = 18}}}
{{{3n = 18}}}
{{{n = 6}}}

Edwin</pre>