document.write( "Question 1209086: Five workers have been hired to complete a job. If one additional worker is hired, they could complete the job 6 days earlier. If the job needs to be completed 32 days earlier, how many additional workers should be hired? \n" ); document.write( "

Algebra.Com's Answer #847655 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "Five workers have been hired to complete a job.
\n" ); document.write( "If one additional worker is hired, they could complete the job 6 days earlier.
\n" ); document.write( "If the job needs to be completed 32 days earlier, how many additional workers should be hired?
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\n" ); document.write( "\n" ); document.write( " Solve it step by step.\r
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document.write( "      Step 1 - determine the number of days needed for 5 workers\r\n" );
document.write( "               to complete the job.\r\n" );
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document.write( "Let d be the number of days for 5 workers to complete the job.\r\n" );
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document.write( "Then the entire job is 5d worker-days.\r\n" );
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document.write( "6 workers could complete the job in (d-6) days.\r\n" );
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document.write( "Hence, from this perspective, the entire work is  6*(d-6)  worker-days.\r\n" );
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document.write( "It gives us this equation\r\n" );
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document.write( "    5d = 6(d-6),\r\n" );
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document.write( "from which we get\r\n" );
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document.write( "     5d = 6d - 36  --->  36 = 6d - 5d  --->  36 = d.\r\n" );
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document.write( "Hence, 5 workers need 36 days to complete the job,  and the entire job is 5*36 = 180 worker-days.\r\n" );
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document.write( "      Step 2 - determine the number of workers needed \r\n" );
document.write( "               to complete the job in 32 days earlier.\r\n" );
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document.write( "The question wants the job be complete in 36-32 = 4 days.\r\n" );
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document.write( "It requires 180/4 = 45 workers.\r\n" );
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document.write( "      Step 3 - determine the number of additional workers \r\n" );
document.write( "               to be hired.\r\n" );
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document.write( "The number of additional workers is  45 - 5 = 40.\r\n" );
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document.write( "ANSWER.  40 additional workers should be hired to complete the job in 32 days earlier.\r\n" );
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