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
Multiplying through by the LCD gives:
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 .
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 or about 17.06 hours.
Edwin