document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1079215>Question 1079215</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 5 men are hired to complete a job. If one more man is hired, the job can be completed 8 days earlier. Assuming that all the men work at the same rate, how many more men should be hired so that the job can be completed 28 days earlier? </SPAN>\n" );
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document.write( "Answer: <font color=red>7 extra workers</font>\r<BR>\n" );
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document.write( "Explanation\r<BR>\n" );
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document.write( "There are many great solutions by the other tutors. <BR>\n" );
document.write( "I'll offer a different viewpoint.\r<BR>\n" );
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document.write( "Consider a job of moving 9000 boxes. <BR>\n" );
document.write( "I'm selecting this number since it's a multiple of 5 and 6, and because it's some large value.<BR>\n" );
document.write( "It turns out that this value 9000 doesn't matter and you can pick any other value to get the same final answer at the end. \r<BR>\n" );
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document.write( "If we had 5 men working to move 9000 boxes, then each man moves 9000/5 = 1800 boxes.<BR>\n" );
document.write( "Each person has a daily unit rate of 1800/x boxes per day where x is the number of days to finish the job with 5 men.<BR>\n" );
document.write( "Note that: rate = (amount done)/time\r<BR>\n" );
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document.write( "Adding a 6th man will mean each person handles 9000/6 = 1500 boxes.<BR>\n" );
document.write( "Each person has a unit rate of 1500/(x-8) since they complete the job 8 days early. \r<BR>\n" );
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document.write( "Assuming each man has the same unit rate, we can equate those fractions.<BR>\n" );
document.write( "Solve 1800/x = 1500/(x-8) to get x = 48. I'll let the student handle the scratch work.<BR>\n" );
document.write( "It will take x = 48 days if you had 5 men on the job.<BR>\n" );
document.write( "The instructions state we want to finish 28 days earlier, so the timeline should be x-28 = 48-28 = 20 days.<BR>\n" );
document.write( "Each worker's unit rate is 1800/x = 1800/48 = 37.5 boxes per day.\r<BR>\n" );
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document.write( "n = number of additional workers to hire in addition to the original 5 men<BR>\n" );
document.write( "n+5 = number of workers total<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( "(37.5 boxes per day)*(20 days) = 9000/(n+5)<BR>\n" );
document.write( "37.5*20 = 9000/(n+5)<BR>\n" );
document.write( "I'll let the student solve that equation. You should arrive at <font color=red>n = 7</font> which is the number of extra workers you should hire so you finish 28 days early.\r<BR>\n" );
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document.write( "More practice found <a  rel=nofollow HREF=\"https://www.algebra.com/algebra/homework/proportions/Proportions.faq.question.1208740.html\">here</a><BR>\n" );
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