document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=962901>Question 962901</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A, B and C together can complete a piece of work in 10 days. All the three started working at it together and after 4 days, A left then B and C together completed the work in 10 more days. A alone can complete the work in? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #588308 by </B><A HREF=/tutors/aboutme.mpl?userid=LinnW><B>LinnW(1048)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=LinnW><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=LinnW><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=588308\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Set a = the rate of A in (piece of work)/day<BR>\n" );
document.write( "    b = the rate of B in (piece of work)/day<BR>\n" );
document.write( "    c = the rate of C in (piece of work)/day\r<BR>\n" );
document.write( "\n" );
document.write( "Below is the equation for all three working together.<BR>\n" );
document.write( "( 10 days ) * ( a + b + c ) = 1(piece of work)<BR>\n" );
document.write( "Next we have the equation were all work together for 4 days,<BR>\n" );
document.write( "then only B and C continue for 10 more days.<BR>\n" );
document.write( "( 4 days) * ( a + b + c ) + (10 days)( b + c) = 1(piece of work)<BR>\n" );
document.write( "Since each left hand side is equal to 1 piece of work,<BR>\n" );
document.write( "we have<BR>\n" );
document.write( "( 10 days ) * ( a + b + c ) = <BR>\n" );
document.write( "( 4 days) * ( a + b + c ) + (10 days)( b + c)<BR>\n" );
document.write( "and<BR>\n" );
document.write( "10( a + b + c ) = 4( a + b + c ) + 10( b + c)<BR>\n" );
document.write( "10a + 10b + 10c = 4a + 4b + 4c + 10b + 10c<BR>\n" );
document.write( "combining terms<BR>\n" );
document.write( "10a + 10b + 10c = 4a + 14b + 14c<BR>\n" );
document.write( "Notice that we can rewrite the above as<BR>\n" );
document.write( "10a + 10(b + c) = 4a + 14(b + c)<BR>\n" );
document.write( "if we subtract 10(b + c) from each side<BR>\n" );
document.write( "10a = 4a + 4(b + c)<BR>\n" );
document.write( "subtract 4a from each side<BR>\n" );
document.write( " 6a = 4(b + c)<BR>\n" );
document.write( "divide each side by 4<BR>\n" );
document.write( " 6a/4 = (b + c)<BR>\n" );
document.write( "Recall<BR>\n" );
document.write( "( 10 days ) * ( a + b + c ) = 1(piece of work) or<BR>\n" );
document.write( "10(a + b + c) = 1<BR>\n" );
document.write( "so<BR>\n" );
document.write( "10a + 10(b + c) = 1<BR>\n" );
document.write( "Now substitute 6a/4 for (b + c) and we have<BR>\n" );
document.write( "10a + 10(6a/4) = 1<BR>\n" );
document.write( "10a + 15a = 1<BR>\n" );
document.write( "25a = 1<BR>\n" );
document.write( "This means that A at rate a will take 25 days to complete the work.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );