Question 1030169

Uncle Donald could do 2 jobs in 3 days and Cousin Kelly could do 4 jobs in 7 days. Cousin Kelly worked alone for 3 days before Uncle Donald joined in. How long would they have to work together to complete a total of 8 jobs?
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Donald rate:: 2/3 job/days 
Kelly rate:: 4/7 job/day 
Together rate::1/x job/day
Kelly in 3 days does 3(4/7) = 12/7 jobs
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Equation:
rate + rate = together rate
2/3 + 4/7 = 1/x
14x + 12x = 21
26x = 21
x = 21/26 days/job
together rate:: 26 job/ 21 day or 1/(21/26) job/day
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Complete 8 jobs if Kelly has completed 12/7 jobs
x(1/(21/26)) = 8 - (12/7)
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26x/21 = (56-12)/7
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26x = 3(44)
x = 5.077 days to finish the 8 houses
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Cheers,
Stan H.
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