document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1206760>Question 1206760</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A contractor undertook to do a certain piece of work in 9 days. He employed certain number of men, but 6 of them being absent from the very first day, the rest could finish the work in 15 days. The number of men originally employed were: </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #844389 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=844389\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the work was originally expected to be done in 9 days.\r<BR>\n" );
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document.write( "the formula i use in problems such as this is:\r<BR>\n" );
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document.write( "p * r * t = q\r<BR>\n" );
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document.write( "p is the number of people<BR>\n" );
document.write( "r is the average rate that each person works at.<BR>\n" );
document.write( "t is the time<BR>\n" );
document.write( "q is the quantity.\r<BR>\n" );
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document.write( "q is usually 1, i.e. 1 job.<BR>\n" );
document.write( "the formula becomes p * r * t = 1\r<BR>\n" );
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document.write( "when the original number of people are working, the formula becomes p * r * 9 = 1\r<BR>\n" );
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document.write( "then 6 are missing, the formula becomes (p-6) * r * 15 = 1\r<BR>\n" );
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document.write( "these 2 equations need to be solved simultaneously.\r<BR>\n" );
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document.write( "start with:<BR>\n" );
document.write( "p * r * 9 = 1<BR>\n" );
document.write( "(p-6) * r * 15 = 1\r<BR>\n" );
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document.write( "divide both sides of the first equation by 9 and divide both sides of the second equation by 15 to get:\r<BR>\n" );
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document.write( "p * r = 1/9<BR>\n" );
document.write( "(p - 6) * r = 1/15\r<BR>\n" );
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document.write( "simplify the second equation and leave the first eqution as is to get:<BR>\n" );
document.write( "p * r = 1/9<BR>\n" );
document.write( "p * r - 6 * r = 1/15\r<BR>\n" );
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document.write( "subtract the second eqution from the first to get:\r<BR>\n" );
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document.write( "6 * r = 1/9 - 1/15.\r<BR>\n" );
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document.write( "place the right side of the equation under the common denominator of 45 to get:\r<BR>\n" );
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document.write( "6 * r = 5/45 - 3/45 = 2/45\r<BR>\n" );
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document.write( "solve for r to get:\r<BR>\n" );
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document.write( "r = 2/45 / 6 = 2/270 which reduces to 1/135.\r<BR>\n" );
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document.write( "now that you have r, you can solve for p.\r<BR>\n" );
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document.write( "p * r * 9 = 1<BR>\n" );
document.write( "when r = 1/135, this becomes p * 1/135 * 9 = 1 <BR>\n" );
document.write( "solve for p to get p = 1 / 9 * 135 = 15.\r<BR>\n" );
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document.write( "the original number of people assigned to the project was 15.\r<BR>\n" );
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document.write( "(p - 6) * r * 15 = 1 becomes:<BR>\n" );
document.write( "(p - 6) * 1/135 * 15 = 1<BR>\n" );
document.write( "solve for (p - 6) to get (p - 6) = 1/15 * 135 = 9.<BR>\n" );
document.write( "solve for p to get p = 15.\r<BR>\n" );
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document.write( "the value of p checks out ok.<BR>\n" );
document.write( "the original number of people assigned to the project is 15.<BR>\n" );
document.write( "after 6 are taken away, the project was then finished with 9.<BR>\n" );
document.write( "the average rate that each person worked is 1/135.\r<BR>\n" );
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document.write( "15 * 1/135 * 9 = 1 is confirmed to be correct.<BR>\n" );
document.write( "9 * 1/135 * 15 = 1 is also confirmed to be correct.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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