<PRE><B>Question 45108</B>
George and Michael working together can do a job in 24 hours. After George being working alone for 7 hours, Michael joined him and together finished the job in 20 more hours. How long would it take each one working alone to do the job? 

George DATA:
Time to do the job= x hrs.; Rate=1/x job per hour

Michael DATA:
Time to do the job= y hrs.; Rate=1/y job per hour

Together Data:
Time to do the job= 24 hrs.; Rate = 1/24 job per hour

EQUATIONS:
rate + rate = rate together
1/x + 1/y = 1/24

george work + together work = 1 job
7 hrs(1/x) +20hrs(1/24) = 1 job
7/x + 5/6 = 1 job
7/x =1/6 job
x=42 hrs. (time for George to do the job alone)

Substitute that into 1/x + 1/y = 1/24 and solve for y, as follows:

1/42 + 1/y = 1/24
(y+42)/42y=1/24
24y+1008=42y
18y=1008
y=56 hrs. ( time for Michael to do the job alone)
Cheers,
Stan H.
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