SOLUTION: Hi, I would really appreciate help with this problem: George and Michael working together can do a job in 24 hours. After George being working alone for 7 hours, Michael join

Question 45108: Hi,
I would really appreciate help with this problem:
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?
Thanks in advance,
Louis
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
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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