SOLUTION: 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 alon

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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
Found 2 solutions by ankor@dixie-net.com, Edwin McCravy:
Answer by ankor@dixie-net.com(22740)   (Show Source): You can put this solution on YOUR website!
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.
:
Let t = time required by Andrew
then
(t+3) = time required by John
:
Let the completed job = 1; (the peeling of 500 lb of potatoes)
:
Each person will do a fraction of job, the two fractions add up to 1
+ = 1
Multiply by t(t+3),
results:
8(t+3) + 8t = t(t+3)
:
8t + 24 + 8t = t^2 + 3t
:
16t + 24 = t^2 + 3t
Arrange as quadratic equation
t^2 + 3t - 16t - 24 = 0
:
t^2 - 13t - 24 = 0
Use the quadratic formula to find t

x=t, a=1, b=-13, c=-24

:

:

The positive solution is what we want here:

t =
t = 14.64 hrs, Andrew working alone
then
14.64+3 = 17.64 hrs, John working alone
:
:
Check solution
+ =
.546 + .454 = 1
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
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


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      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



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

Solution:  .

Those two solutions are approximately 

 and 

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
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