document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=678628>Question 678628</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A,B and C working together can do a certain task in 6 hours. A & B can do the task in 9 hours, and B & C can do the task in 12 hours. How long would it take each working alone to do the task? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #421564 by </B><A HREF=/tutors/aboutme.mpl?userid=ptaylor><B>ptaylor(2198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ptaylor><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=ptaylor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=421564\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x=amount of time needed for A do do the task working alone<BR>\n" );
document.write( "Then A works at the rate of 1/x of the task per hour<BR>\n" );
document.write( "Let y=amount of time needed for B to do the task working alone<BR>\n" );
document.write( "Then B works at the rate of 1/y of the task per hour<BR>\n" );
document.write( "Let z=amount of time needed for C to do the task working alone<BR>\n" );
document.write( "Then C works at the rate of 1/z of the task per hour\r<BR>\n" );
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document.write( "A,B,C working together works at the rate of (1/x)+(1/y)+(1/z) of the task per hour and this equals (1/6)\r<BR>\n" );
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document.write( "(1/x)+(1/y)+(1/z)=(1/6)------------------eq 1<BR>\n" );
document.write( "(1/x)+(1/y)=(1/9)------------------------eq2<BR>\n" );
document.write( "(1/y)+(1/z)=(1/12)-------------------------eq3\r<BR>\n" );
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document.write( "Substitute (1/9) from eq2 for ((1/x)+(1/y)) in eq1<BR>\n" );
document.write( "(1/9)+(1/z)=(1/6)<BR>\n" );
document.write( "(1/z)=(3/18)-(2/18)=(1/18); z=18 hr----time needed for C working alone<BR>\n" );
document.write( "Substitute (1/18) for (1/z) in eq3<BR>\n" );
document.write( "(1/y)+(1/18)=(1/12)<BR>\n" );
document.write( "(1/y)=(3/36)-(2/36)=(1/36); y=36 hr-----time needed for B working alone<BR>\n" );
document.write( "Substitute (1/36) for (1/y) in eq2<BR>\n" );
document.write( "(1/x)+(1/36)=(1/9)<BR>\n" );
document.write( "(1/x)=(4/36)-(1/36)=(3/36)=(1/12); x=12 hrs---time needed for A working alone\r<BR>\n" );
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document.write( "CK<BR>\n" );
document.write( "(1/12)+(1/36)+(1/18)=(1/6)=(6/36)<BR>\n" );
document.write( "(3/36)+(1/36)+(2/36)=(6/36)<BR>\n" );
document.write( "(6/36)=(6/36)\r<BR>\n" );
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document.write( "Hope this helps---ptaylor\r<BR>\n" );
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document.write( " </SPAN>\n" );
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