document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=148509>Question 148509</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose it takes Tom and Dick 2 hours to do a certain job, it takes Tom and Harry 3 hours to do the same job. It takes Dick and Harry 4 hours to do this same job.\r<BR>\n" );
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document.write( "How long will it take Tom, Dick, and Harry to do the same job together? \r<BR>\n" );
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document.write( "So, just for organizing: <BR>\n" );
document.write( "T + D = 2hrs<BR>\n" );
document.write( "T + H = 3hrs<BR>\n" );
document.write( "D + H = 4hrs<BR>\n" );
document.write( "T+D+H = ? hrs\r<BR>\n" );
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document.write( "Therefore: (I think, but I'm sure it's most probably right) <BR>\n" );
document.write( "1/T + 1/D =1/2<BR>\n" );
document.write( "1/T + 1/H =1/3<BR>\n" );
document.write( "1/D + 1/H =1/4<BR>\n" );
document.write( "1/T + 1/D + 1/H =1/x\r<BR>\n" );
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document.write( "So far, I got to T=12/5 and D=12<BR>\n" );
document.write( "using reciprocals and the first equation, the sum is 6/12 or 1/2; so far so good.<BR>\n" );
document.write( "But I've tried using it to solve for the H one.. and it doesn't quite work.. so when I get to the last equation I still have two variables, H and X.\r<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 #108838 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=108838\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Suppose it takes Tom and Dick 2 hours to do a certain job, it takes Tom and Harry 3 hours to do the same job. It takes Dick and Harry 4 hours to do this same job. <BR>\n" );
document.write( "How long will it take Tom, Dick, and Harry to do the same job together? <BR>\n" );
document.write( "So, just for organizing: <BR>\n" );
document.write( "T + D = 2hrs<BR>\n" );
document.write( "T + H = 3hrs<BR>\n" );
document.write( "D + H = 4hrs<BR>\n" );
document.write( "T+D+H = ? hrs <BR>\n" );
document.write( "Therefore: (I think, but I'm sure it's most probably right) <BR>\n" );
document.write( "1/T + 1/D =1/2<BR>\n" );
document.write( "1/T + 1/H =1/3<BR>\n" );
document.write( "1/D + 1/H =1/4<BR>\n" );
document.write( "1/T + 1/D + 1/H =1/x <BR>\n" );
document.write( "So far, I got to T=12/5 and D=12<BR>\n" );
document.write( "using reciprocals and the first equation, the sum is 6/12 or 1/2; so far so good.<BR>\n" );
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document.write( "You only need the 1st three equations.<BR>\n" );
document.write( "Three equations with three unknows yields an answer:<BR>\n" );
document.write( "1/T + 1/D + 0   = 1/2<BR>\n" );
document.write( "1/T + 0   +1/H  =1/3<BR>\n" );
document.write( "o   +1/D  + 1/H =1/4<BR>\n" );
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document.write( "1/T = 7/24<BR>\n" );
document.write( "1/D = 5/24<BR>\n" );
document.write( "1/H = 1/24<BR>\n" );
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document.write( "So T time = 24/7 = 3 3/7 days<BR>\n" );
document.write( "D time = 24/5 = 4 4/5 days<BR>\n" );
document.write( "H time = 24 days<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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