document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1167923>Question 1167923</A>: <I><SPAN STYLE=\"word-break: break-all;\"> One roofer can put a new roof on a house three times faster than another. Working together they can roof a house in 5 days. How long would it take the faster roofer working alone? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #792515 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=792515\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> rate * time = quantity.\r<BR>\n" );
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document.write( "let x = the rate of the slower roofer.\r<BR>\n" );
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document.write( "then 3x = the rate of the faster roofer.\r<BR>\n" );
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document.write( "when they work together their rates are additive and they can roof a house in 5 days.\r<BR>\n" );
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document.write( "quantity = 1 roof\r<BR>\n" );
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document.write( "formula becomes:\r<BR>\n" );
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document.write( "(x + 3x) * 5 = 1<BR>\n" );
document.write( "combine like terms to get:<BR>\n" );
document.write( "4x * 5 = 1<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "20x = 1<BR>\n" );
document.write( "solve for x to get:<BR>\n" );
document.write( "x = 1/20\r<BR>\n" );
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document.write( "that's the rate of the slower roofer.\r<BR>\n" );
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document.write( "the rate of the roofer is 3 times that = 3/20 of the job per day.\r<BR>\n" );
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document.write( "when the faster roofer is working alone, the equation becomes:\r<BR>\n" );
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document.write( "3/20 * time = 1\r<BR>\n" );
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document.write( "solve for time to get:\r<BR>\n" );
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document.write( "time = 20/3\r<BR>\n" );
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document.write( "the faster roofer, working alone, can roof a house in 20/3 days.\r<BR>\n" );
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document.write( "that would be 6 and 2/3 days.\r<BR>\n" );
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document.write( "that should be your answer. *****\r<BR>\n" );
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document.write( "to go a few steps further, .....\r<BR>\n" );
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document.write( "when the slower roofer works alone, the formula becomes:\r<BR>\n" );
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document.write( "1/20 * time = 1\r<BR>\n" );
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document.write( "solve for time to get:\r<BR>\n" );
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document.write( "time = 20 days.\r<BR>\n" );
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document.write( "the faster roofer completes the job in 6 and 2/3 days, working alone.<BR>\n" );
document.write( "the slower roofer completes the job in 20 days, working alone.\r<BR>\n" );
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document.write( "it takes the slower work 3 times as long to complete the job as the faster worker.\r<BR>\n" );
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document.write( "that's because the faster worker is 3 times as fast as the slower worker.\r<BR>\n" );
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document.write( "everything checks out.\r<BR>\n" );
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document.write( "your solution is good.<BR>\n" );
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