Question 335677
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/N+1/E}}} of the job
since the job takes 6 hours for both working together then
{{{6*(1/N+1/E)=1  }}}
{{{6*(1/(2*E)+1/E)=1}}}   (substitute N=2*E or E=N/2)
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Solve for E
{{{6(1/(2*E)+2/(2*E))=1}}}   (common denominator)
{{{6(3/(2*E))=1}}}
9/E=1
E=9 hours