Question 63092
 Deirdre, Tara, and Caitlin can complete a certain job in 5 days. Deirdre can do the job alone in 12 days. Tara can do the job alone in 10 days. How many days would it take Caitlin alone to complete the job?
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Let the completed job = 1:
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Let x = C"s time alone
:
{{{5/12 + 5/10 + 5/x}}} = 1
You can tell by the value of the 1st two fractions that C' contribution to the job will not be much:
:
Mult eq by a common denominator; 60x would be a good one, resulting in
5x(5) + 6x(5) + 60(5) = 60x
25x + 30x + 300 = 60x
25x + 30x - 60x = - 300
-5x = -300
x = -300/-5
x = 60 hrs for C to do the job by herself!!
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Check:
{{{5/12 + 5/10 + 5/60}}} = 1