document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=956559>Question 956559</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a man does half as much work as his son in three - four of the time .if they take 18 days to complete the work .how many days will take to do work alone </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #584469 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=584469\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the general equation is rate * time = quantity of work.<BR>\n" );
document.write( "the quantity of the work is equal to 1 job.<BR>\n" );
document.write( "for the son, you get:\r<BR>\n" );
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document.write( "r * t = 1\r<BR>\n" );
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document.write( "solve for r to get r = 1/t\r<BR>\n" );
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document.write( "for the father you get:\r<BR>\n" );
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document.write( "r * 3/4 * t = 1/2\r<BR>\n" );
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document.write( "solve for r to get r = 4/6t which can be simplified to 2/3t\r<BR>\n" );
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document.write( "the ratio of the father's rate to the son's rate is 2/3t divided by 1/t.\r<BR>\n" );
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document.write( "this is the same as 2/3t * t which results in 2/3.\r<BR>\n" );
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document.write( "the father works at 2/3 the rate as the son.\r<BR>\n" );
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document.write( "when they work together, they can finish a job in 18 days.\r<BR>\n" );
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document.write( "you get:\r<BR>\n" );
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document.write( "t = 18\r<BR>\n" );
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document.write( "rate of the son = r\r<BR>\n" );
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document.write( "rate of the father = 2/3 * r\r<BR>\n" );
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document.write( "q is equal to 1.\r<BR>\n" );
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document.write( "when they work together, their rates are additive.\r<BR>\n" );
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document.write( "you get:\r<BR>\n" );
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document.write( "(r + 2/3 * r) * 18 = 1\r<BR>\n" );
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document.write( "use this equation to solve for r.\r<BR>\n" );
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document.write( "you get:\r<BR>\n" );
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document.write( "(3/3 * r + 2/3 * r) * 18 = 1\r<BR>\n" );
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document.write( "combine like terms to get:\r<BR>\n" );
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document.write( "5/3 * r * 18 = 1\r<BR>\n" );
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document.write( "simplify further to get:\r<BR>\n" );
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document.write( "(5 * 18)/3 * r = 1\r<BR>\n" );
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document.write( "simplify further to get:\r<BR>\n" );
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document.write( "30 * r = 1\r<BR>\n" );
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document.write( "solve for r to get r = 1/30.\r<BR>\n" );
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document.write( "that's the rate of the son.\r<BR>\n" );
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document.write( "the rate of the father is 2/3 * r which is equal to 2/90 which can be simplified to 1/45.\r<BR>\n" );
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document.write( "you have:\r<BR>\n" );
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document.write( "rate of the son is 1/30 of the job in 1 hour.<BR>\n" );
document.write( "rate of the father is 1/45 of the job in 1 hour.\r<BR>\n" );
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document.write( "to confirm, replace these rates in the equation where both of them are working together to get:\r<BR>\n" );
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document.write( "(r + 2/3 * r) * 18 = 1\r<BR>\n" );
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document.write( "the equation becomes:\r<BR>\n" );
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document.write( "(1/30 + 1/45) * 18 = 1 which becomes:\r<BR>\n" );
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document.write( "(3/90 + 2/90) * 18 = 1 which becomes:\r<BR>\n" );
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document.write( "5/90 * 18 = 1 which becomes:\r<BR>\n" );
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document.write( "90/90 = 1 which becomes 1 = 1.\r<BR>\n" );
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document.write( "the rates are confirmed as good.\r<BR>\n" );
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document.write( "you now know the rates of the father and the son.\r<BR>\n" );
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document.write( "the question is:\r<BR>\n" );
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document.write( "how many days will it take to do the work alone.\r<BR>\n" );
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document.write( "the same equation is used, but now their rates are separate.\r<BR>\n" );
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document.write( "for the son:\r<BR>\n" );
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document.write( "r * t = q becomes 1/30 * t = 1 which gets you t = 30 days.\r<BR>\n" );
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document.write( "for the father:\r<BR>\n" );
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document.write( "r * t = q becomes 1/45 * t = 1 which gets you t = 45 days.\r<BR>\n" );
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document.write( "working together, they can do the job in 18 days.\r<BR>\n" );
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document.write( "working separately, the son can do the job in 30 days and the father can do the job in 45 days.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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