document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=914657>Question 914657</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A mason and his assistant work together for 4 hours on a brick fireplace before the mason has to leave the job. The assistant finishes the job alone in 10 hours. If the mason can construct a fireplace in 12 hours working alone, how long does it take his assistant working alone to construct a fireplace?\r<BR>\n" );
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document.write( "I know this is a work problem and r*t=wc. If the problem was straight forward I would set it up as X/10 + x/12 =1 but how do i account for the fours hours already worked together? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #555226 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39620)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=555226\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Work-problems like this are a type of Uniform Rates problem.  Try this equational format:   RT=J for rate, time, amount of job.  The rates are in dimension of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=JOBS%2FTIME ALIGN=MIDDLE  ALT=\"JOBS%2FTIME\"   DISABLED_style= \"max-width:90%; height:auto;\" > for 1 unit of time, usually.\r<BR>\n" );
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document.write( "Look at the rates for these workers.<BR>\n" );
document.write( "Mason,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F12 ALIGN=MIDDLE  ALT=\"1%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Assistant,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fx ALIGN=MIDDLE  ALT=\"1%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Mason+Assistant,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F12%2B1%2Fx ALIGN=MIDDLE  ALT=\"1%2F12%2B1%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The sum of their individual rates is their rate when they work together.  We do not yet know the time needed for the assistant to do this 1 job alone; but I am calling this time, x.\r<BR>\n" );
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document.write( "The arrangement of the time and the workers was to do 1 whole job.  They work together 4 hours and then assistant works alone to finish in 10 hours.\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%281%2F12%2B1%2Fx%294%2B%281%2Fx%29%2A10=1%29 ALIGN=MIDDLE  ALT=\"highlight%28%281%2F12%2B1%2Fx%294%2B%281%2Fx%29%2A10=1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The question essentially asks for finding the value of x.<BR>\n" );
document.write( "See the way the equation uses the uniform rates rule!<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28RateTogether%29%28TimeTogether%29%2B%28RateAssistant%29%28TimeAssistantWorked%29=ONEWHOLEJOB ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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