Question 1030169
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: {{{3/2}}} = 1.5 days per job
Kelly: {{{7/4}}} = 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
{{{((t+3))/1.75}}} + {{{t/1.5}}} = 8
multiply equation by the least common denominator; 2.625
2.625*{{{((t+3))/1.75}}} + 2.625*{{{t/1.5}}} = 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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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