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" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #693548 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=693548\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the general formula used in this type of problem is:\r<BR>\n" );
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document.write( "prt = q\r<BR>\n" );
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document.write( "p is the number of people<BR>\n" );
document.write( "r is the rate at which each person works<BR>\n" );
document.write( "t is the amount of time<BR>\n" );
document.write( "q is the quantity of work produced.\r<BR>\n" );
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document.write( "in your problem:\r<BR>\n" );
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document.write( "t = number of days.<BR>\n" );
document.write( "q = 1 job\r<BR>\n" );
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document.write( "you get:\r<BR>\n" );
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document.write( "5rt = 1<BR>\n" );
document.write( "6r(t-8) = 1\r<BR>\n" );
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document.write( "the first equation says:<BR>\n" );
document.write( "5 people working at a certain rate for each person for a certain amount of days = 1 job.\r<BR>\n" );
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document.write( "the second equation says:<BR>\n" );
document.write( "5 people working at the same rate for each person for 8 less than a certain amount of days = 1 job.\r<BR>\n" );
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document.write( "use the first equation to solve for r in terms of t.\r<BR>\n" );
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document.write( "you get r = 1/(5t)\r<BR>\n" );
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document.write( "replace r with 1/(5t) in the second equation to get:\r<BR>\n" );
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document.write( "6 * 1/(5t) * (t-8) = 1\r<BR>\n" );
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document.write( "multiply both sides of this equation by 5t to get:\r<BR>\n" );
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document.write( "6 * (t-8) = 5t\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "6t - 48 = 5t\r<BR>\n" );
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document.write( "subtract 5t from both sides of this equation to get:\r<BR>\n" );
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document.write( "6t - 5t = 48\r<BR>\n" );
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document.write( "solve for t to get t = 48.\r<BR>\n" );
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document.write( "your first equation of 5rt = 1 becomes 5 * r * 48 = 1\r<BR>\n" );
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document.write( "solve for r to get r = 1 / (5 * 48)\r<BR>\n" );
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document.write( "simplify to get r = 1/240\r<BR>\n" );
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document.write( "you now should know the value of the variables involved.\r<BR>\n" );
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document.write( "you have:\r<BR>\n" );
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document.write( "r = 1/240<BR>\n" );
document.write( "t = 48\r<BR>\n" );
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document.write( "in the equation of 5rt = 1, you get 5 * 1/240 * 48 = 1 which results in 1 = 1 which is true.\r<BR>\n" );
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document.write( "in the equation of 6r(t-8) = 1, you get 6 * 1/240 * 40 = 1 which results in 1 = 1 which is true.\r<BR>\n" );
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document.write( "you can now solve for the number of people required to finish the job 28 days earlier.\r<BR>\n" );
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document.write( "the same equation is used.\r<BR>\n" );
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document.write( "prt = 1\r<BR>\n" );
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document.write( "r = 1/240\r<BR>\n" );
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document.write( "since t = 45, then t - 28 becomes 48 - 28 which becomes 20.\r<BR>\n" );
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document.write( "you need to solve for p\r<BR>\n" );
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document.write( "the equation of prt = 1 becomes p * 1/240 * 20 = 1\r<BR>\n" );
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document.write( "solve for p to get p = 240 / 20 = 12\r<BR>\n" );
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document.write( "you would need 12 people to finish the job 28 days earlier.\r<BR>\n" );
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document.write( "formula is prt = 1\r<BR>\n" );
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document.write( "p = 12<BR>\n" );
document.write( "r = 1/240<BR>\n" );
document.write( "t = 20\r<BR>\n" );
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document.write( "12 * 1/240 * 20 = 1 becomes 1 = 1 which is true.\r<BR>\n" );
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document.write( "i believe your solution will be that 12 people are required.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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