SOLUTION: 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 w

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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?
---I have an idea of what must be done to solve this problem, but I need clarification. An explanation would be amazing. Thanks!
Found 3 solutions by ankor@dixie-net.com, ptaylor, stanbon:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Uncle Donald could do 2 jobs in 3 days and Cousin Kelly could do 4 jobs in 7 days.
Find how long each will take to do one job
Donald: 3%2F2 = 1.5 days per job
Kelly: 7%2F4 = 1.75 days per job
:
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?
let t = how long they need to work together to complete 8 jobs
%28%28t%2B3%29%29%2F1.75 + t%2F1.5 = 8
multiply equation by the least common denominator; 2.625
2.625*%28%28t%2B3%29%29%2F1.75 + 2.625*t%2F1.5 = 2.625(8)
Cancel the denominators
1.5(t+3) + 1.75t = 21
1.5t + 4.5 + 1.75t = 21
3.25t = 21 - 4.5
3.25t = 16.5
t = 16.5/3.25
t = 5.1 days working together
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:
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Confirm this solution: Kelly worked 5.1 + 3 = 8.1 days
8.1/1.75 = 4.6 jobs
5.1/1.5 + 3.4 jobs
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total jobs: 8.0

Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=amount of time it takes working together for them to complete a total of 8 jobs
Uncle Donald works at the rate of 2/3 of the job per day
Cousin Kelly works at the rate of 4/7 of the job per day
In three days, Cousin Kelly did (4/7)*3=12/7 of the jobs, leaving (8=56/7)
(56/7 - 12/7)=44/7 of the jobs yet to be completed
Working together, they work at the rate of (2/3)+(4/7)=(14/21)+(12/21)=26/21 of the jobs per day
Soooooo our equation to solve is:
(26/21)*x=44/7 multiply each side by 21 to get rid of fractions
26x=132
x=5.08 days
hope this helps----ptaylor

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!

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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