document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=855307>Question 855307</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If 80 men dug 4 holes in 12 months, how many men would be required to dig 6 holes in 4 month? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #515237 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=515237\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If 80 men dug 4 holes in 12 months, how many men would be required to dig 6 holes in 4 month?\r<BR>\n" );
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document.write( "80 men dug 4 holes in 12 months.<BR>\n" );
document.write( "divide that by 12 and you get 80 men dug 1/3 of a hole in 1 month.<BR>\n" );
document.write( "divide that by 80 and you get 1 man dug 1/240 of a hole in one month.\r<BR>\n" );
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document.write( "does this make sense?<BR>\n" );
document.write( "let's see.<BR>\n" );
document.write( "1 man digs 1/240 of a hole in one month.<BR>\n" );
document.write( "working at the same rate, that same man can dig 12/240 of a hole in 12 months.<BR>\n" );
document.write( "80 men, working at the same rate per man, can dig (12 * 80) / 240 of a hole in 12 months.\r<BR>\n" );
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document.write( "(12 * 80) / 240 = 960 / 12 = 4, so:<BR>\n" );
document.write( "80 men, working at the same rate per man, can dig 4 holes in 12 months.\r<BR>\n" );
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document.write( "formula makes sense, so we'll use it.\r<BR>\n" );
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document.write( "the formula can be condensed to:\r<BR>\n" );
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document.write( "rate of work that each man produces * number of men * time = units of work produced.\r<BR>\n" );
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document.write( "this can be abbreviated to r * n * t = u<BR>\n" );
document.write( "r = rate of work that each man produces.<BR>\n" );
document.write( "n = number of men.<BR>\n" );
document.write( "t = time.<BR>\n" );
document.write( "u = units of work produced.\r<BR>\n" );
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document.write( "time for this problem is in months.<BR>\n" );
document.write( "units of work produced are the holes in the ground.\r<BR>\n" );
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document.write( "we start with the first statement in the problem:<BR>\n" );
document.write( "80 men dug 4 holes in 12 months.<BR>\n" );
document.write( "the units of work produced is 4 holes<BR>\n" );
document.write( "the rate of work for each man is unknown so we'll keep it at r<BR>\n" );
document.write( "the number of men is given as 80.<BR>\n" );
document.write( "the time they took to do the work is given as 12 months.\r<BR>\n" );
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document.write( "the formula of r * n * t = u becomes:<BR>\n" );
document.write( "r * 80 * 12 = 4<BR>\n" );
document.write( "solve for r to get:<BR>\n" );
document.write( "r = 4 / (80 * 12) = 4/960 = 1/240.\r<BR>\n" );
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document.write( "so far we have:\r<BR>\n" );
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document.write( "r = 1/240<BR>\n" );
document.write( "n = 80<BR>\n" );
document.write( "t = 12<BR>\n" );
document.write( "u = 4\r<BR>\n" );
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document.write( "to confirm we did this correctly, we check the original equation out with those numbers to see if the equation is true.\r<BR>\n" );
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document.write( "we get:<BR>\n" );
document.write( "r * n * t = u becomes:<BR>\n" );
document.write( "1/240 * 80 * 12 = 4<BR>\n" );
document.write( "simplifying this equation, we get:<BR>\n" );
document.write( "240 = 240 which is true indicating we did this part of the problem correctly.\r<BR>\n" );
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document.write( "this part of the problem found the value of r which we will use in the next part of the problem.\r<BR>\n" );
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document.write( "we now look at the second part of the problem.\r<BR>\n" );
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document.write( "that part is the question:<BR>\n" );
document.write( "how many men would be required to dig 6 holes in 4 months.\r<BR>\n" );
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document.write( "the basic formula is the same.<BR>\n" );
document.write( "r * n * t = u<BR>\n" );
document.write( "r = 1/240 that we solved for earlier (the rate that each person works is assumed to be the same).<BR>\n" );
document.write( "n = n because we don't know what this is at the present time.<BR>\n" );
document.write( "t = 4 months<BR>\n" );
document.write( "u = 6 holes\r<BR>\n" );
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document.write( "we plug these values into the equation to get:<BR>\n" );
document.write( "1/240 * n * 4 = 6\r<BR>\n" );
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document.write( "we solve for n to get:<BR>\n" );
document.write( "n = 6 / (1/240 * 4) which becomes n = 6 / (4/240) which becomes n = 6 * 240/4 which becomes n = 6 * 60 which becomes 360.\r<BR>\n" );
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document.write( "if we did this correctly, then it would take 360 men to fill 6 holes in 4 months.\r<BR>\n" );
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document.write( "we confirm whether this is true or not by replacing n with 360 in the original equation to get:<BR>\n" );
document.write( "1/240 * n * 4 = 6 becomes:<BR>\n" );
document.write( "1/240 * 360 * 4 = 6<BR>\n" );
document.write( "we simplify to get:<BR>\n" );
document.write( "6 = 6 confirming that our calculation of the number of people required is good.\r<BR>\n" );
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document.write( "the answer is that it would require 360 men to fill 6 holes in 4 months.\r<BR>\n" );
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