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

{{{(matrix(4,1,
"John's", rate, in, "jobs/hour"))}}}{{{""+""}}}{{{(matrix(4,1,
"Andrew's", rate, in, "jobs/hour"))}}}{{{""=""}}}{{{(matrix(5,1,
Their, combined,rate, in, "jobs/hour"))}}}

{{{1/(x+2)}}}{{{""+""}}}{{{1/x}}}{{{""=""}}}{{{1/8}}}

Multiplying through by the LCD gives:

{{{x^2-14x-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 +- sqrt(65)}}}.
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 + sqrt(65)}}} or about 17.06 hours. 

Edwin</pre>