document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1066074>Question 1066074</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 8 workers can paint a building in 24 days.How many days will 18 workers take to paint the same building </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #681255 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=681255\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> this can be an inverse variation type problem.<BR>\n" );
document.write( "the formula to use is y = k/x<BR>\n" );
document.write( "set y = 24 days and set x = 8 workers and solve for k.<BR>\n" );
document.write( "you get 24 = k/8<BR>\n" );
document.write( "solve for k to get k = 192\r<BR>\n" );
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document.write( "k is the constant of variation and will always remain the same.<BR>\n" );
document.write( "when x = 18, the formula becomes y = 192/18.<BR>\n" );
document.write( "solve for y to get y = 10 and 2/3 days.\r<BR>\n" );
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document.write( "to see if this is correct, use the rate of each person * number of people * time = quantity of work formula.\r<BR>\n" );
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document.write( "when people paint 1 building in 24 days, this formula becomes:\r<BR>\n" );
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document.write( "r * 8 * 24 = 1\r<BR>\n" );
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document.write( "r is the rate of each person.<BR>\n" );
document.write( "8 is the number of people.<BR>\n" );
document.write( "24 is the number of days.<BR>\n" );
document.write( "1 is the quantity of work produced (1 painted building).\r<BR>\n" );
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document.write( "solve for r to get r = 1 / (8 * 24)<BR>\n" );
document.write( "you get r = 1/192.\r<BR>\n" );
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document.write( "when the number of people is 18 and the rate of each person is 1/192, the formula becomes:\r<BR>\n" );
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document.write( "1/192 * 18 * t = 1\r<BR>\n" );
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document.write( "1/192 is the rate of each person.<BR>\n" );
document.write( "this means each person paints 1/192 of the building in one day.<BR>\n" );
document.write( "18 is the number of people painting.<BR>\n" );
document.write( "t is the number of days<BR>\n" );
document.write( "1 is the quantity of work produced (1 painted building).\r<BR>\n" );
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document.write( "solve for t to get t = 1 / (18 * 1/192)<BR>\n" );
document.write( "simplify to get t = 1 / (18/192)<BR>\n" );
document.write( "this is equivalent to t = 1 * 192/18<BR>\n" );
document.write( "simplify to get t = 192/18<BR>\n" );
document.write( "convert to a mixed fraction to get t = 10 and 2/3 days.\r<BR>\n" );
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document.write( "the answer is the same whether you use the inverse variation formula or the rate of each person * number of people * time = quantity of work produced formula.\r<BR>\n" );
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document.write( "your solution should be 10 and 2/3 days.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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