document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1103341>Question 1103341</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Working together, Mr. Kent and Mr. Wayne can complete a job in 5 hours.  If Mr. Wayne takes twice as long as Mr. Kent if each does the job alone, how long does it take Mr. Kent to complete the job alone?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #718061 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=718061\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> rate * time = quantity of wrok performed is the equation that you can use to solve this.\r<BR>\n" );
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document.write( "let k be the rate that mr. kent works at.<BR>\n" );
document.write( "let w be the rate that mr. wayne works at.<BR>\n" );
document.write( "let 1 represent the quantity of work performed which is 1 job.<BR>\n" );
document.write( "let T represent the time it takes.\r<BR>\n" );
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document.write( "your equation becomes:\r<BR>\n" );
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document.write( "(k + w) * T = 1\r<BR>\n" );
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document.write( "since T = 5, the equation becomes (k + w) * 5 = 1\r<BR>\n" );
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document.write( "you are given that mr. kent takes twice as long as mr. wayne to do the job alone.\r<BR>\n" );
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document.write( "this means that mr. wayne must be working twice as fast as mr. kent.\r<BR>\n" );
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document.write( "the rate for mr. wayne is 2 times the rate for mr. kent.\r<BR>\n" );
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document.write( "therefore, you get w = 2k.\r<BR>\n" );
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document.write( "your original formula of (k + w) * 5 = 1 becomes (k + 2k) * 5 = 1 after you replace w with 2k.\r<BR>\n" );
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document.write( "the formula becomes 3k * 5 = 1\r<BR>\n" );
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document.write( "solve for k to get k = 1/15.\r<BR>\n" );
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document.write( "since w = 2k, then w = 2/15.\r<BR>\n" );
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document.write( "mr. kent can complete 1/15 of the job in 1 hour.<BR>\n" );
document.write( "mr. wayne can complete 2/15 of the job in 1 hour.\r<BR>\n" );
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document.write( "their combined rate is (k + w) = 1/15 + 2/15) = 3/15 of the job in 1 hour.\r<BR>\n" );
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document.write( "you get 3/15 * 5 = 1 which results in 1 = 1 which confirms the calculated rates for mr. kent and mr. wayne are correct.\r<BR>\n" );
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document.write( "when he is working alone, the formula for mr. kent becomes 1/15 * T = 1.<BR>\n" );
document.write( "solve for T to get T = 15.<BR>\n" );
document.write( "it would take mr. kent 15 hours to complete the job alone.\r<BR>\n" );
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document.write( "when he is working alone, the formula for mr. wayns becomes 2/15 * T = 1.<BR>\n" );
document.write( "solve for T to get T = 7.5.<BR>\n" );
document.write( "it would take mr kent 7.5 hours to complete the job alone.<BR>\n" );
document.write( "that's twice as fast as it would take mr. kent working alone.\r<BR>\n" );
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