document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=934502>Question 934502</A>: <I><SPAN STYLE=\"word-break: break-all;\"> With this question: \"If 6 men can do a piece of work in 14 days, how many men are needed to do the work in 21 days?\" How do I know when to solve it with proportions (x=9 version 1) versus with man-days (x=4 version 2) as shown below?\r<BR>\n" );
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document.write( "Version 1:<BR>\n" );
document.write( "if 6 men/14 days than, than x men/21 days [set-up as a proportion problem]<BR>\n" );
document.write( "6 men/14 days = x men/21 days [set the ratios equal to each other and cross-multiply]<BR>\n" );
document.write( "(6)(21)=14x<BR>\n" );
document.write( "126=14x [solve for x]<BR>\n" );
document.write( "x=9<BR>\n" );
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document.write( "Version 2:<BR>\n" );
document.write( "If 6 men can do the piece of work in 14 days, then one man requires (6)(14) or 84 days to do it. In<BR>\n" );
document.write( "other words, the job takes 84 man-days<BR>\n" );
document.write( " 1 man takes 84 days<BR>\n" );
document.write( " 2 men takes 42 days<BR>\n" );
document.write( " 4 men takes 21 days <BR>\n" );
document.write( "Let x= number of men required to do the job in 21 days <BR>\n" );
document.write( "21 times x = number of man-days required to do the job and that equals 84 <BR>\n" );
document.write( "21x=84<BR>\n" );
document.write( " x=4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #567554 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=567554\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Part of solving this one is to be able to recognize that it is a UNIFORM RATES problem.  It takes the form of R*T=J for rate, time, job.  The rate also depends on how many agents are participating to do any part of the job.\r<BR>\n" );
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document.write( "Assume all men work individually at an equal rate, calling this rate r, in units of JOBS PER DAYS.  The 1 job is \"a piece of work\".  The men being described will in the way they are distributed, complete ONE job.\r<BR>\n" );
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document.write( "\"If 6 men can do a piece of work in 14 days, how many men are needed to do the work in 21 days?\"\r<BR>\n" );
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document.write( "Let r be the rate for one man.<BR>\n" );
document.write( "Let n be the unknown number of men to find.<BR>\n" );
document.write( "Let j be 1 for ONE WHOLE JOB.<BR>\n" );
document.write( "Uniform rates rule here would be of the form, R*t=j, where R depends on the number of men, workers, or agents doing any quantity of job.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%286r%29%2A14=1=%28n%2Ar%29%2A21%29 ALIGN=MIDDLE  ALT=\"highlight%28%286r%29%2A14=1=%28n%2Ar%29%2A21%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That should now make sense.  <BR>\n" );
document.write( "Solve for n.\r<BR>\n" );
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document.write( "---<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286%2A14%2Ar%29%2F%28r%2A21%29=n ALIGN=MIDDLE  ALT=\"%286%2A14%2Ar%29%2F%28r%2A21%29=n\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=%286%2A14%29%2F21 ALIGN=MIDDLE  ALT=\"n=%286%2A14%29%2F21\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=%286%2A2%2A7%29%2F%283%2A7%29 ALIGN=MIDDLE  ALT=\"n=%286%2A2%2A7%29%2F%283%2A7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=2%2A2 ALIGN=MIDDLE  ALT=\"n=2%2A2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28n=4%29 ALIGN=MIDDLE  ALT=\"highlight%28n=4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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