SOLUTION: Mark, Lex, and Bren can finish a job 12,16, and 19 hours, respectively. Mark and Lex worked together for 4 hours. Lex got tired so Bren worked in place of him until the job is fini

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Question 1165824: Mark, Lex, and Bren can finish a job 12,16, and 19 hours, respectively. Mark and Lex worked together for 4 hours. Lex got tired so Bren worked in place of him until the job is finished. How long did Mark work?
Found 2 solutions by Boreal, Edwin McCravy:
Answer by Boreal(15235) (Show Source):
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in one hour, Mark does 1/12, Lex 1/16, and Bren 1/19 of the job
In 4 hours, Mark did 4/12, Lex 4/16
That is 1/3 + 1/4 of the job or 7/12
Mark needs to work x more hours to do x/12, and Bren x hours to do x/19
that sum is 5/12
(x/12)+(x/19)=5/12
multiply by 228,
19x+12x=95
31x=95
x=3.06 hours
so Mark worked 7.06 hours and did 58.8% of the job
Lex worked 4 hours and did 25% of the job
Bren worked 3.06 hours and did 3.06/19 or 16.1% of the job
Within rounding error, this is the 100%

Answer by Edwin McCravy(20060) (Show Source):
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Make the following chart. Fill in the times, letting the time that only Mark and Bren worked together after Lex quit be t. When they did the whole job themselves we put 1 for the part of a job done, which means 100% of the job was done. | Part of | Rate | Time | | job | in | taken | | done | jobs/hr | in hrs | ------------------------------------ Mark | 1 (all)| | 12 | Lex | 1 | | 16 | Bren | 1 | | 19 | ------------------------------------ Mark | | | 4 | Lex | | | 4 | Mark | | | t | Bren | | | t | First we use the top three to get expressions for their rates by dividing the part of job done (1) by the time. | Part of | Rate | Time | | job | in | taken | | done | jobs/hr | in hrs | ------------------------------------ Mark | 1 (all)| 1/12 | 12 | Lex | 1 | 1/16 | 16 | Bren | 1 | 1/19 | 19 | ------------------------------------ Mark | | 1/12 | 4 | Lex | | 1/16 | 4 | Mark | | 1/12 | t | Bren | | 1/19 | t | Next we multiply the the rates by the time to get the parts of a job done. | Part of | Rate | Time | | job | in | taken | | done | jobs/hr | in hrs | ------------------------------------ Mark | 1 (all)| 1/12 | 12 | Lex | 1 | 1/16 | 16 | Bren | 1 | 1/19 | 19 | ------------------------------------ Mark | 4/12 | 1/12 | 4 | Lex | 4/16 | 1/16 | 4 | Mark | t/12 | 1/12 | t | Bren | t/19 | 1/19 | t | Those four parts of a job below the second dotted line must add to be 1 job. Reduce the fractions that will reduce: Multiply through by LCD of 228 That's the number of hours he worked with Bren. The total time Mark worked was the 4 hours he worked with Lex only plus the 3.064516129 hours he worked with Bren only after Lex quit or 7.064516129 hours. <--answer Edwin