Question 327804
John takes 3 hours longer than Andrew to
peel 500 pounds (lb) of apples. If together they can peel
500 lb of apples in 8 hours, then how long would it take
each one working alone
<pre><b>

This is a slightly different approach. The other tutor added
up fractions of a job in one hour.  I take it from a rate
approach, whene their rate together equals the sum of their
individual rates.  Either way is correct.  I just prefer this
method.


Make this chart


               Number of      Time       Rate  
               batches of      in         in
                apples        hours    batches/hr  
-------------------------------------------------
John alone         
Andrew alone       
Both together     

Let Andrew's time working alone be x.  We fill that in:


               Number of      Time       Rate  
               batches of      in         in
                apples        hours    batches/hr
-------------------------------------------------  
John alone        
Andrew alone                    x        
Both together                   

>>...John takes 3 hours longer than Andrew...<<

So John's time working alone is x+3, so we fill that in.

               Number of      Time       Rate  
               batches of      in         in
                apples        hours    batches/hr  
-------------------------------------------------
John alone                     x+3       
Andrew alone                    x        
Both together                         

>>...together they can peel 500 lb of apples in 8 hours...<<

So we fill that in for the time for both together:

               Number of      Time       Rate  
               batches of      in         in
                apples        hours    batches/hr  
-------------------------------------------------
John alone                     x+3       
Andrew alone                    x        
Both together                   8        

In all three cases exactly 1 batch (500 lbs) of apples are peeled. 
So we put 1's for the number of batches of apples peeled. 

               Number of      Time       Rate  
               batches of      in         in
                apples        hours    batches/hr  
-------------------------------------------------
John alone         1           x+3       
Andrew alone       1            x        
Both together      1            8        

Now we form the three rates by Rate = {{{number_of_batches/hours}}}


               Number of      Time       Rate  
               batches of      in         in
                apples        hours    batches/hr 
------------------------------------------------- 
John alone         1           x+3       1/(x+3)
Andrew alone       1            x        1/x
Both together      1            8        1/8


Now we make the equation by:

         John's alone rate + Andrew's rate alone = Rate of both together

               1/(x+3)     +        1/x          =         1/8

{{{1/(x+3)}}}{{{""+""}}}{{{1/x}}}{{{""=""}}}{{{1/8}}}

Can you solve that by first getting the LCD? If not post again asking how.

Solution:  {{{(13 +- sqrt(265))/2}}}.

Those two solutions are approximately 

{{{x}}}{{{""=""}}}{{{14.6394103}}} and {{{x}}}{{{""=""}}}{{{-1.639410298}}}

We ignore the negative answer and conclude that Andrew's time
alone is about 14.6 hours and since John takes 3 hours longer,
or about 14.6 + 3 = 17.6 hours.

Edwin</pre>