document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=313753>Question 313753</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A building contractor employs a master mason, a journeyman mason and an apprentice mason.<BR>\n" );
document.write( "The master mason and the journeyman working together can finish a brick wall in 10 hours. It<BR>\n" );
document.write( "takes the master and apprentice 12 hours to do the same job, while the journeyman and apprentice<BR>\n" );
document.write( "require 15 hours to complete the task.<BR>\n" );
document.write( "If all three work together, how long does it take to build the wall? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #224421 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=224421\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A building contractor employs a master mason, a journeyman mason and an apprentice mason.<BR>\n" );
document.write( "The master mason and the journeyman working together can finish a brick wall in 10 hours. <BR>\n" );
document.write( "It takes the master and apprentice 12 hours to do the same job,<BR>\n" );
document.write( " while the journeyman and apprentice require 15 hours to complete the task.<BR>\n" );
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document.write( "Find how many hrs each require working alone<BR>\n" );
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document.write( "Let the individual times of the three masons be: m, j, a<BR>\n" );
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document.write( "Let the completed job = 1<BR>\n" );
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document.write( "Write an equation for each statement:<BR>\n" );
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document.write( "\"The master mason and the journeyman working together can finish a brick wall in 10 hours\"<BR>\n" );
document.write( "Eq1:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2Fm ALIGN=MIDDLE  ALT=\"10%2Fm\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2Fj ALIGN=MIDDLE  ALT=\"10%2Fj\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( ":<BR>\n" );
document.write( "\"It takes the master and apprentice 12 hours to do the same job,\"<BR>\n" );
document.write( "Eq2:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2Fm ALIGN=MIDDLE  ALT=\"12%2Fm\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2Fa ALIGN=MIDDLE  ALT=\"12%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
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document.write( "\"the journeyman and apprentice require 15 hours to complete the task.\"<BR>\n" );
document.write( "Eq3:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2Fj ALIGN=MIDDLE  ALT=\"15%2Fj\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2Fa ALIGN=MIDDLE  ALT=\"15%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
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document.write( "Multiply Eq1 by 6 and Eq2 by 5:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60%2Fm ALIGN=MIDDLE  ALT=\"60%2Fm\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60%2Fj ALIGN=MIDDLE  ALT=\"60%2Fj\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 6<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60%2Fm ALIGN=MIDDLE  ALT=\"60%2Fm\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60%2Fa ALIGN=MIDDLE  ALT=\"60%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 5<BR>\n" );
document.write( "-------------------------------Subtraction eliminates m, so we have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60%2Fj ALIGN=MIDDLE  ALT=\"60%2Fj\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60%2Fa ALIGN=MIDDLE  ALT=\"60%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
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document.write( "Multiply eq3 by 4 and add to the above equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60%2Fj ALIGN=MIDDLE  ALT=\"60%2Fj\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60%2Fa ALIGN=MIDDLE  ALT=\"60%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60%2Fj ALIGN=MIDDLE  ALT=\"60%2Fj\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60%2Fa ALIGN=MIDDLE  ALT=\"60%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 4<BR>\n" );
document.write( "----------------------------- adding eliminates a, find j<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=120%2Fj ALIGN=MIDDLE  ALT=\"120%2Fj\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 5<BR>\n" );
document.write( "5j = 120<BR>\n" );
document.write( "j = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=120%2F5 ALIGN=MIDDLE  ALT=\"120%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "j = 24 hrs to do the job alone<BR>\n" );
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document.write( "Substitute 24 for j in eq1, find m<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2Fm ALIGN=MIDDLE  ALT=\"10%2Fm\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2F24 ALIGN=MIDDLE  ALT=\"10%2F24\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( "Multiply by 24m<BR>\n" );
document.write( "10(24) + 10m = 24m<BR>\n" );
document.write( "240 = 24m - 10m<BR>\n" );
document.write( "m = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=240%2F14 ALIGN=MIDDLE  ALT=\"240%2F14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "m = 17.14 hrs to do the job alone<BR>\n" );
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document.write( "Using eq3, find a<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2F24 ALIGN=MIDDLE  ALT=\"15%2F24\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2Fa ALIGN=MIDDLE  ALT=\"15%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( "Multiply by 24a<BR>\n" );
document.write( "15a + 15(24) = 24a<BR>\n" );
document.write( "360 = 24a - 15a<BR>\n" );
document.write( "a = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=360%2F9 ALIGN=MIDDLE  ALT=\"360%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a = 40 hrs to do the job alone<BR>\n" );
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document.write( "Summarize: a = 40; j = 24; m = 17.14 hrs<BR>\n" );
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document.write( "\"If all three work together, how long does it take to build the wall?\"<BR>\n" );
document.write( "Let t = time required when all three work together<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%2F17.14 ALIGN=MIDDLE  ALT=\"t%2F17.14\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%2F24 ALIGN=MIDDLE  ALT=\"t%2F24\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%2F40 ALIGN=MIDDLE  ALT=\"t%2F40\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( "multiply equation by 17.14*24*40 = 16454.4, results:<BR>\n" );
document.write( "960t + 685.6t + 411.36t = 16454.4<BR>\n" );
document.write( "2056.96t = 16454.4<BR>\n" );
document.write( "t = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16454.4%2F2056.96 ALIGN=MIDDLE  ALT=\"16454.4%2F2056.96\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "t ~ 8 hrs all three working<BR>\n" );
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document.write( "Check solution using a calc:<BR>\n" );
document.write( "8/17.14 + 8/24 + 8/40 =<BR>\n" );
document.write( ".467 + .333 + .2 = 1<BR>\n" );
document.write( " </SPAN>\n" );
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