document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1124934>Question 1124934</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A new machine makes 20,000 aluminum cans three times faster than an older machine. With both machines operating, it takes 6 h to make 20,000 cans. How long would it take the new machine, working alone, to make 20,000 cans? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #741227 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=741227\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> rate * time = quantity of work produced.\r<BR>\n" );
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document.write( "the rate of the new machine is 3 times the rate of the old machine.\r<BR>\n" );
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document.write( "if the rate of the old machine is x, then the rate of the new machine is 3x.\r<BR>\n" );
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document.write( "when both machines work together, their rates are additive.\r<BR>\n" );
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document.write( "therefore:\r<BR>\n" );
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document.write( "(x + 3x) * time = quantity of work produced.\r<BR>\n" );
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document.write( "time is 6 hours and quantity of work produced is 20,000, therefore:\r<BR>\n" );
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document.write( "(x + 3x) * 6 = 20,000.\r<BR>\n" );
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document.write( "combine like terms to get 4x * 6 = 20,000\r<BR>\n" );
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document.write( "\divide both both sides of the equation by 24 to get:\r<BR>\n" );
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document.write( "x = 20,000 / 24 = 833 and 1/3.\r<BR>\n" );
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document.write( "3x is therefore 3 * (833 + 1/3) = 2500\r<BR>\n" );
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document.write( "to see if these rates are accurate, replace x and 3x in the original equation to see if it holds truel.\r<BR>\n" );
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document.write( "the original equation is (x + 3x) * 6 = 20,000.\r<BR>\n" );
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document.write( "substituting 833 and 1/3 for x and 2500 for 3x, we get:\r<BR>\n" );
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document.write( "((833 + 1/3) + 2500) * 6 = 25,000.\r<BR>\n" );
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document.write( "this results in 25,000 = 25,000, which is true, therefore you can assume that the rates are accurate.\r<BR>\n" );
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document.write( "given that the rate of the new machbine is 2500 aluminum cans per hour, then the formula for the new machine is 2500 * time = 20,000.\r<BR>\n" );
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document.write( "this results in time = 20,000 / 2500 = 8 hours.\r<BR>\n" );
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document.write( "the new machine would take 8 hours working alone.\r<BR>\n" );
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document.write( "breaking down the 6 hours when working together, you get:\r<BR>\n" );
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document.write( "(833 + 1/3) * 6 = 5000 aluminum cans in 6 hours.\r<BR>\n" );
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document.write( "2500 * 6 = 15000 aluminum cans in 6 hours.\r<BR>\n" );
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document.write( "total for 6 hours = 20,000 cans.\r<BR>\n" );
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document.write( "the new machine, at 3 times the rate of the old machine, produced 3 times the number of cans in the same 6 hours.\r<BR>\n" );
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document.write( "your solution is that the new machine would take 8 hours to make 20,000 aluminum cans, working alone.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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