document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=958724>Question 958724</A>: <I><SPAN STYLE=\"word-break: break-all;\"> if 15 machines do the work in 105 days then how many days are required for same work by 35 machines? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #585918 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=585918\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> this looks like it can be solved with an inverse ratio.\r<BR>\n" );
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document.write( "inverse ratio formula is y = k / x\r<BR>\n" );
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document.write( "first you find k.\r<BR>\n" );
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document.write( "then you use k to find your solution.\r<BR>\n" );
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document.write( "let y = days and x equal number of machines.\r<BR>\n" );
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document.write( "when y = 105 and x = 15, you get 105 = k / 15.\r<BR>\n" );
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document.write( "solve for k to get k = 105 * 15 = 1575\r<BR>\n" );
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document.write( "that's your constant of variation.\r<BR>\n" );
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document.write( "that remains the same.\r<BR>\n" );
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document.write( "when x = 35, the equation becomes y = 1575 / 35.\r<BR>\n" );
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document.write( "solve for y to get y = 45.\r<BR>\n" );
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document.write( "with 15 machines running, it takes 105 days.\r<BR>\n" );
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document.write( "with 35 machines running, it takes 45 days.\r<BR>\n" );
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document.write( "you could also solve this by using the rate per machine * number of machines * time = quantity formula.\r<BR>\n" );
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document.write( "let quantity equal 1 job.<BR>\n" );
document.write( "let number of machines = 15<BR>\n" );
document.write( "let time = 105 days.\r<BR>\n" );
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document.write( "formula becomes:\r<BR>\n" );
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document.write( "rate per machine * 15 * 105 days = 1\r<BR>\n" );
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document.write( "solve for rate per machine to get rate per machine = 1 / (15 * 105).\r<BR>\n" );
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document.write( "rate per machine is equal to 1 / (15 * 105) of the job completed in one day.\r<BR>\n" );
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document.write( "how many days would it take 35 machines to do the job?\r<BR>\n" );
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document.write( "number of machines is now 35.<BR>\n" );
document.write( "rate per machine is still 1 / (15 * 105).<BR>\n" );
document.write( "quantity is still 1.\r<BR>\n" );
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document.write( "formula becomes:\r<BR>\n" );
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document.write( "35 * 1 / (15 * 105) * number of days = 1\r<BR>\n" );
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document.write( "solve for number of days to get:\r<BR>\n" );
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document.write( "number of days = (1 * 15 * 105) / 35 which is equal to 45 days.\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( "the inverse ratio formula is y = k / x.\r<BR>\n" );
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document.write( "the number of machines * rate of each machine * time = quantity formula can be shown as:\r<BR>\n" );
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document.write( "r * m * t = q\r<BR>\n" );
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document.write( "r = rate per machine<BR>\n" );
document.write( "m = number of machines<BR>\n" );
document.write( "t = time<BR>\n" );
document.write( "q = quantity of work.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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