SOLUTION: Hello! An experienced accountant can balance the books twice as fast as a new accountant. Working together it takes the accountants 6 hours. How long would it take the experienc

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Question 335677: Hello!
An experienced accountant can balance the books twice as fast as a new accountant. Working together it takes the accountants 6 hours. How long would it take the experienced accountant working alone?

Thanks!

Answer by jrfrunner(365) About Me  (Show Source):
You can put this solution on YOUR website!
An experienced accountant can balance the books twice as fast as a new accountant. Working together it takes the accountants 6 hours. How long would it take the experienced accountant working alone?
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Let E=time taken by experienced accountant
Let N=time taken by new accountant
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Given: An experienced accountant can balance the books twice as fast as a new accountant.
Therefore N=2*E or E=N/2
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Let 1/N = proportion of job completed by New accountant in "one" hour
Let 1/E = proportion of job completed by Experienced accountant in "one" hour
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"Every" hour working "together" they will accomplish
1%2FN%2B1%2FE of the job
since the job takes 6 hours for both working together then
6%2A%281%2FN%2B1%2FE%29=1++
6%2A%281%2F%282%2AE%29%2B1%2FE%29=1 (substitute N=2*E or E=N/2)
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Solve for E
6%281%2F%282%2AE%29%2B2%2F%282%2AE%29%29=1 (common denominator)
6%283%2F%282%2AE%29%29=1
9/E=1
E=9 hours