document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=964905>Question 964905</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If 20 men can complete a piece of job in 8days, how long will it take 10 men to finish the job working at the same rate </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #589705 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=589705\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> this is an inverse ratio type problem.<BR>\n" );
document.write( "it is also a rate per person * number of people * time = quantity type problem.<BR>\n" );
document.write( "you can solve it either way.\r<BR>\n" );
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document.write( "with inverse ratio, you will get:\r<BR>\n" );
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document.write( "y = k/x is the standard inverse ratio formula.\r<BR>\n" );
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document.write( "when y = 8 days, x = 20 men.\r<BR>\n" );
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document.write( "use the formula to compute k.\r<BR>\n" );
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document.write( "you will get 8 = k/20\r<BR>\n" );
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document.write( "solve for k to get:\r<BR>\n" );
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document.write( "k = 20*8 = 160\r<BR>\n" );
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document.write( "k remains constant.\r<BR>\n" );
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document.write( "when x = 10 men, the formula becomes:\r<BR>\n" );
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document.write( "y = 160 / 10 which becomes:\r<BR>\n" );
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document.write( "y = 16 days.\r<BR>\n" );
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document.write( "this stands to reason.\r<BR>\n" );
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document.write( "half the men should take twice as long and they do.\r<BR>\n" );
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document.write( "now solve using the rate per person * number of people * time = quantity formula.\r<BR>\n" );
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document.write( "that formula is abbreviated as r * p * t = q\r<BR>\n" );
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document.write( "20 men can finish the job in 10 days.\r<BR>\n" );
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document.write( "rate per person is to be calculated using 20 people and 8 days and a quantity of 1 job.\r<BR>\n" );
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document.write( "the formula becomes r * 20 * 8 = 1\r<BR>\n" );
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document.write( "solve for r to get 4 = 1/(20*8) = 1/160\r<BR>\n" );
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document.write( "each person can complete 1/160 of the job in 1 day.\r<BR>\n" );
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document.write( "does that make sense?\r<BR>\n" );
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document.write( "20 people working at the individual rate of 1/160 of the job in 1 day and taking 8 days would complete 1/160 * 20 * 8 = 1/160 * 160 = 160/160 of the job which is equal to 1 job.\r<BR>\n" );
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document.write( "so we have r = 1/160 of the job in one day per person.\r<BR>\n" );
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document.write( "use that formula to figure out the time required to do one job if only 10 people were working.\r<BR>\n" );
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document.write( "you get r*p*t = q becomes:\r<BR>\n" );
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document.write( "1/160 * 10 * t = 1\r<BR>\n" );
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document.write( "solve for t to get:\r<BR>\n" );
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document.write( "t = 1 / (1/160 * 10) which becomes:\r<BR>\n" );
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document.write( "t = 1 / (1/16) which becomes:\r<BR>\n" );
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document.write( "t = 1 * (16/1) which becomes:\r<BR>\n" );
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document.write( "t = 16\r<BR>\n" );
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document.write( "both formulas get you the same answer.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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