SOLUTION: John takes 2 hours longer than Andrew to peel 600 pounds of apples. If together they can peel 600 pounds of apples in 8 hours, then how long would it take John to peel the ap

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Question 1039949: John takes 2 hours longer than Andrew to peel 600 pounds
of apples. If together they can peel 600 pounds of apples
in 8 hours, then how long would it take John to peel the
apples working alone?
Found 2 solutions by stanbon, Edwin McCravy:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
John takes 2 hours longer than Andrew to peel 600 pounds of apples. If together they can peel 600 pounds of apples in 8 hours, then how long would it take John to peel the apples working alone?
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Andrew DATA:: time = x hrs/job ; rate = 1/x job/hr
John DATA: time = x+2 hrs/job ; rate = 1/(x+2) job/hr
------------
Together DATA:: time = 8 hrs/job ; rate = 1/8 job/hr
-----
Equation:
rate + rate = together rate
1/x + 1/(x+2) = 1/8
-----
8(x+2) + 8x = x(x+2)
16x + 16 = x^2 + 2x
----
x^2 - 14x - 16 = 0
----
x = 15.06 hrs (time for Andrew alone)
x+2 = 17.06 hrs (time for John alone)
-------------
Cheers,
Stan H.
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Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!
John takes 2 hours longer than Andrew to peel 600 pounds
of apples. If together they can peel 600 pounds of apples
in 8 hours, then how long would it take John to peel the
apples working alone?

For simplicity, we will re-label the peeling of 600 pounds 
of apples as "1 job".  Then the problem is stated:

John takes 2 hours longer than Andrew to do 1 job. If
together they can do 1 job in 8 hours, then how long would
it take John to do 1 job working alone? 
From that we can make this chart, letting Andrew's time for
1 job be x hours, and John's time to be x+2 hours.

                      | Jobs done |  rate in jobs/hr | time in hrs      
------------------------------------------------------------------
John working alone    |     1     |                  |    x+2
Andrew working alone  |     1     |                  |     x
Both working together |     1     |                  |     8

Then we fill in the rate in jobs/hr, by dividing jobs by time in hours:

                      | Jobs done |  rate in jobs/hr | time in hrs      
------------------------------------------------------------------
John working alone    |     1     |     1/(x+2)      |    x+2
Andrew working alone  |     1     |       1/x        |     x
Both working together |     1     |       1/8        |     8

%28matrix%284%2C1%2C%0D%0A%22John%27s%22%2C+rate%2C+in%2C+%22jobs%2Fhour%22%29%29%22%22%2B%22%22%28matrix%284%2C1%2C%0D%0A%22Andrew%27s%22%2C+rate%2C+in%2C+%22jobs%2Fhour%22%29%29%22%22=%22%22%28matrix%285%2C1%2C%0D%0ATheir%2C+combined%2Crate%2C+in%2C+%22jobs%2Fhour%22%29%29

1%2F%28x%2B2%29%22%22%2B%22%221%2Fx%22%22=%22%221%2F8

Multiplying through by the LCD gives:

x%5E2-14x-16+=+0

Solve that for x, which is Andrew's time, then add 2 to find John's time.
You'll have to use the quadratic formula.  You get 7+%2B-+sqrt%2865%29.
Discard the negative answer and the positive answer is about 15.06 hours.
So Andrew's time is about 15.06 hours and John's time is 2 hours longer
or 9+%2B+sqrt%2865%29 or about 17.06 hours. 

Edwin