Question 1025775
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a welder requires 24 hours to do a job. After the welder and apprentice  work on the job for 12 hours, the welder quits. The apprentice finished the job in 9 hours. How long would it take the apprentice, working alone, to do the job?
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Let a = the rate-of-work (in units of {{{job/hour}}}) of the apprentice.

We know that the welder's rate-of-work is {{{1/24}}} of the job-per-hour.

The balance equation is 

{{{9a}}} = {{{1 - 12*(1/24 + a))}}}.

Simplify it:

9a = {{{1/2}}} - 12a,

21a = {{{1/2}}},

a = {{{1/(2*21)}}} = {{{1/42}}}.

Hence, it will take 42 hours for the apprentice to complete the job working alone.
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