document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=407455>Question 407455</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If it takes workers A and B 2 days to complete a job. And it takes workers B and C 3 days to complete the same job. And it takes workers A and C 4 days to complete this job how long does it take each worker to do this job alone. And what formulas are used. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #287375 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=287375\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If it takes workers A and B 2 days to complete a job.<BR>\n" );
document.write( " And it takes workers B and C 3 days to complete the same job.<BR>\n" );
document.write( " And it takes workers A and C 4 days to complete this job how long does it take<BR>\n" );
document.write( " each worker to do this job alone.<BR>\n" );
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document.write( "Let a, b, c, represent the time required by each work alone<BR>\n" );
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document.write( "Let the completed job = 1<BR>\n" );
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document.write( "Write a shared work equation for each statement:<BR>\n" );
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document.write( "\"If it takes workers A and B 2 days to complete a job.\"<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Fa ALIGN=MIDDLE  ALT=\"2%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Fb ALIGN=MIDDLE  ALT=\"2%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( ":<BR>\n" );
document.write( "\"If it takes workers B and C 3 days to complete the same job.\"<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Fb ALIGN=MIDDLE  ALT=\"3%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Fc ALIGN=MIDDLE  ALT=\"3%2Fc\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
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document.write( "\"it takes workers A and C 4 days to complete this job\"<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Fa ALIGN=MIDDLE  ALT=\"4%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Fc ALIGN=MIDDLE  ALT=\"4%2Fc\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
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document.write( "Add all three equations to give us another equation to work with<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Fa ALIGN=MIDDLE  ALT=\"2%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Fb ALIGN=MIDDLE  ALT=\"2%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%2Fc ALIGN=MIDDLE  ALT=\"0%2Fc\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%2Fa ALIGN=MIDDLE  ALT=\"0%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Fb ALIGN=MIDDLE  ALT=\"3%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Fc ALIGN=MIDDLE  ALT=\"3%2Fc\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Fa ALIGN=MIDDLE  ALT=\"4%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%2Fb ALIGN=MIDDLE  ALT=\"0%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Fc ALIGN=MIDDLE  ALT=\"4%2Fc\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( "---------------------------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Fa ALIGN=MIDDLE  ALT=\"6%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2Fb ALIGN=MIDDLE  ALT=\"5%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2Fc ALIGN=MIDDLE  ALT=\"7%2Fc\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 3<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Multiply the 1st equation by 3, subtract the above equation from it<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Fa ALIGN=MIDDLE  ALT=\"6%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Fb ALIGN=MIDDLE  ALT=\"6%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%2Fc ALIGN=MIDDLE  ALT=\"0%2Fc\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 3<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Fa ALIGN=MIDDLE  ALT=\"6%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2Fb ALIGN=MIDDLE  ALT=\"5%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2Fc ALIGN=MIDDLE  ALT=\"7%2Fc\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 3<BR>\n" );
document.write( "---------------------------------------subtraction eliminates a<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%2Fa ALIGN=MIDDLE  ALT=\"0%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fb ALIGN=MIDDLE  ALT=\"1%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2Fc ALIGN=MIDDLE  ALT=\"7%2Fc\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0<BR>\n" );
document.write( ":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fb ALIGN=MIDDLE  ALT=\"1%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2Fc ALIGN=MIDDLE  ALT=\"7%2Fc\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Cross multiply<BR>\n" );
document.write( "c = 7b<BR>\n" );
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document.write( "In equation: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Fb ALIGN=MIDDLE  ALT=\"3%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Fc ALIGN=MIDDLE  ALT=\"3%2Fc\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1, replace c with 7b<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Fb ALIGN=MIDDLE  ALT=\"3%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F7b ALIGN=MIDDLE  ALT=\"3%2F7b\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( "Multiply by 7b, results<BR>\n" );
document.write( "7(3) + 3 = 7b<BR>\n" );
document.write( "21 + 3 = 7b<BR>\n" );
document.write( "24 = 7b<BR>\n" );
document.write( "b = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%2F7 ALIGN=MIDDLE  ALT=\"24%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "b = 3.43 hrs, B alone<BR>\n" );
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document.write( "Find c<BR>\n" );
document.write( "c = 7b<BR>\n" );
document.write( "c = 7(3.43)<BR>\n" );
document.write( "c = 24 hrs, C alone<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Find a using, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Fa ALIGN=MIDDLE  ALT=\"4%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Fc ALIGN=MIDDLE  ALT=\"4%2Fc\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1; replace c with 24<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Fa ALIGN=MIDDLE  ALT=\"4%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F24 ALIGN=MIDDLE  ALT=\"4%2F24\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( "multiply by 24a<BR>\n" );
document.write( "24(4) + 4a = 24a<BR>\n" );
document.write( "96 = 24a - 4a<BR>\n" );
document.write( "96 = 20a<BR>\n" );
document.write( "a = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=96%2F20 ALIGN=MIDDLE  ALT=\"96%2F20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a = 4.8 hrs, A alone<BR>\n" );
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document.write( "Check this in the 1st equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F4.8 ALIGN=MIDDLE  ALT=\"2%2F4.8\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3.43 ALIGN=MIDDLE  ALT=\"2%2F3.43\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1 <BR>\n" );
document.write( ".42 + .58 = 1 confirms our solutions of:<BR>\n" );
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document.write( "A = 4.8 hrs, B = 3.43 hrs, C = 24 hrs (almost useless) \r<BR>\n" );
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document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );