document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1208740>Question 1208740</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Five workers have been hired to complete a job.  If one additional worker is hired, they could complete the job 10 days earlier.  If the job needs to be completed 32 days earlier, how many additional workers should be hired? </SPAN>\n" );
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document.write( "I have edited your question to remove the dollar signs.<BR>\n" );
document.write( "It seems to be a strange copy/paste error.<BR>\n" );
document.write( "My method isn't as efficient compared with tutor Edwin's method, but it's another viewpoint to think about at least.\r<BR>\n" );
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document.write( "Let's say the job is moving 9000 boxes. <BR>\n" );
document.write( "The number 9000 can be changed to any positive whole number and the final answer will be the same. <BR>\n" );
document.write( "I'm picking this value since it's a multiple of 5 and 6.\r<BR>\n" );
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document.write( "We have these two key assumptions:<BR>\n" );
document.write( "1. Each worker moves boxes at the same rate.<BR>\n" );
document.write( "2. None of the workers slow down any others. \r<BR>\n" );
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document.write( "If there are 9000 boxes, and 5 workers on the job, then each person handles 9000/5 = 1800 boxes.<BR>\n" );
document.write( "x = number of days to finish the job if there are 5 workers <BR>\n" );
document.write( "rate*time = amount done<BR>\n" );
document.write( "rate = (amount done)/time<BR>\n" );
document.write( "rate = 1800/x\r<BR>\n" );
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document.write( "If there are 5 workers, each handling 1800 boxes, then each person moves 1800/x boxes per day. <BR>\n" );
document.write( "This is the unit rate per worker. \r<BR>\n" );
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document.write( "Now introduce another worker to have 5+1 = 6 workers.<BR>\n" );
document.write( "Each worker now handles 9000/6 = 1500 boxes.\r<BR>\n" );
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document.write( "This extra worker brings the original number of days x to x-10 since this expanded group can complete the job 10 days earlier.<BR>\n" );
document.write( "We find the unit rate per worker is 1500/(x-10) boxes per day.\r<BR>\n" );
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document.write( "Using assumption #1 mentioned earlier, we can solve 1800/x = 1500/(x-10) to get x = 60 which is the number of days it takes if you had 5 workers.<BR>\n" );
document.write( "We determine that the unit rate per worker is 1800/x = 1800/60 = 30 boxes per day (or you could compute it like this 1500/(x-10) = 1500/(60-10) = 30)<BR>\n" );
document.write( "Also we determine it takes x-10 = 60-10 = 50 days if you had 6 workers.\r<BR>\n" );
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document.write( "We want the job to finish 32 days early, so we want the duration to be x-32 = 60-32 = 28 days instead of the initial 60.<BR>\n" );
document.write( "n = number of extra workers you need to hire<BR>\n" );
document.write( "n+5 = number of workers you'll have total when considering the initial 5<BR>\n" );
document.write( "9000/(n+5) = number of boxes each worker handles\r<BR>\n" );
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document.write( "rate*time = amount done<BR>\n" );
document.write( "(30 boxes per day)*(28 days) = 9000/(n+5)<BR>\n" );
document.write( "30*28 = 9000/(n+5)<BR>\n" );
document.write( "840 = 9000/(n+5)<BR>\n" );
document.write( "840*(n+5) = 9000<BR>\n" );
document.write( "840n+4200 = 9000<BR>\n" );
document.write( "840n = 9000 - 4200<BR>\n" );
document.write( "840n = 4800<BR>\n" );
document.write( "n = 4800/840<BR>\n" );
document.write( "n = 5.7142857 approximately<BR>\n" );
document.write( "Note that the mixed number 5 & 5/7 is equal to 5.7142857 approximately, so this matches what Edwin got.<BR>\n" );
document.write( "Obviously it's not possible to hire 0.714 of a worker, so we need to round up to n = 6. It's likely some of the workers won't have much to do as the job is getting closer to the end. \r<BR>\n" );
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document.write( "Answer: <font color=red>6 additional workers</font>\r<BR>\n" );
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document.write( "A similar question found <a  rel=nofollow HREF=\"https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1079215.html\">here</a> and also <a  rel=nofollow HREF=\"https://www.algebra.com/algebra/homework/Rate-of-work-word-problems/Rate-of-work-word-problems.faq.question.1208470.html\">here</a><BR>\n" );
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