document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=684987>Question 684987</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A can do a piece of work in 24 days, B in 32 days and C in 64 days. all begin to do it together, but A leaves after 6 days and B leaves 6 days before the completion of work. how many days did the work last ? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #424305 by </B><A HREF=/tutors/aboutme.mpl?userid=Jolliano><B>Jolliano(16)</B></A><img src=\"/images/stars/stars-06.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Jolliano><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=Jolliano><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=424305\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A = 24 days<BR>\n" );
document.write( "B = 32 days<BR>\n" );
document.write( "C = 64 days.\r<BR>\n" );
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document.write( "Fraction of work done in one day<BR>\n" );
document.write( "by A = 1/24<BR>\n" );
document.write( "by B = 1/32<BR>\n" );
document.write( "by C = 1/64.\r<BR>\n" );
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document.write( "During the six days before A leaves,the fraction of the work that has been done is <BR>\n" );
document.write( "6/24 = 1/4 by A<BR>\n" );
document.write( "6/32 = 3/16 by B<BR>\n" );
document.write( "6/64 = 3/32 by C.\r<BR>\n" );
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document.write( "Total fraction of work done in First 6 days =<BR>\n" );
document.write( "1/4 + 3/16 + 3/32<BR>\n" );
document.write( "=(8 + 6 + 3)/32<BR>\n" );
document.write( "= 17/32.\r<BR>\n" );
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document.write( "Fraction of work left = 1 -17/32 = 15/32.\r<BR>\n" );
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document.write( "Since B leaves 6 days before the completion of the work,it means that C works alone for 6 days. The fraction of work C does alone in those 6 days is<BR>\n" );
document.write( "6/64 = 3/32.\r<BR>\n" );
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document.write( "Therefore fraction of work done before B's departure =<BR>\n" );
document.write( "15/32 - 3/32 = 12/32<BR>\n" );
document.write( "=3/8.\r<BR>\n" );
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document.write( "Let X be the number of days in which B and C did 3/8 of the work.\r<BR>\n" );
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document.write( "Therefore,<BR>\n" );
document.write( "x/32 is done by B<BR>\n" );
document.write( "and x/64 is done by C.\r<BR>\n" );
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document.write( "This shows that<BR>\n" );
document.write( "x/32 + x/64 = 3/8<BR>\n" );
document.write( "Multiply through by 64<BR>\n" );
document.write( "2x + x = 3 * 8<BR>\n" );
document.write( "3x = 24<BR>\n" );
document.write( "x = 24/3 = 8 days. <BR>\n" );
document.write( "Total number of days<BR>\n" );
document.write( "= 6 + 8 + 6 = 20 days.  </SPAN>\n" );
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