document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=568937>Question 568937</A>: <I><SPAN STYLE=\"word-break: break-all;\">  If a wall was built by 4 men and 2 women in 5 days<BR>\n" );
document.write( "how many days it will take to built by 3 men and 1 women? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #367171 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=367171\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you don't provide any information about how fast each is working, so the assumption is that they all work at the same rate.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if the wall is built by 4 men and 2 women in 5 days, then you calculate their rate of work (how fast they work and their rate of work are used to talk about the same thing) as follows:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "rate * time = units of work.<BR>\n" );
document.write( "the number of units is 1 (the wall).<BR>\n" );
document.write( "the rate that they work is x (we don't know it yet).<BR>\n" );
document.write( "the time is 5 days.<BR>\n" );
document.write( "we get rate * time = units of work equation becomes:<BR>\n" );
document.write( "x * 5 = 1<BR>\n" );
document.write( "we divide both sides of the equation by 5 to get:<BR>\n" );
document.write( "x = 1/5<BR>\n" );
document.write( "the 4 men and 2 women, all working together, have a speed or rate of work that is equivalent to building 1/5 of the wall per day.<BR>\n" );
document.write( "if you divide the rate by the number of people, then you get:<BR>\n" );
document.write( "1/5 divided by 6 = 1/5 * 1/67 = 1/30.<BR>\n" );
document.write( "this means that each person builds 1/30 of the wall per day.<BR>\n" );
document.write( "confirm your equation by going back to the original problem.<BR>\n" );
document.write( "rate * time = units of work.<BR>\n" );
document.write( "the units of work is equal to 1 (the wall).<BR>\n" );
document.write( "the rate per person is 1/30 of the wall per day.<BR>\n" );
document.write( "the number of people is 6.<BR>\n" );
document.write( "the equation becomes:<BR>\n" );
document.write( "6 * 1/30 * time = 1<BR>\n" );
document.write( "this becomes:<BR>\n" );
document.write( "6/30 * time = 1<BR>\n" );
document.write( "multiply both sides of this equation by 30/6 to get:<BR>\n" );
document.write( "time = 30/6 * 1 which becomes:<BR>\n" );
document.write( "time = 5 days.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the equation works with the original situation.<BR>\n" );
document.write( "now reduce the number of men and women to 4.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the equation becomes:<BR>\n" );
document.write( "4 * 1/30 * time = 1 which becomes 4/30 * time = 1<BR>\n" );
document.write( "multiply both sides of this equation by 30/4 to get:<BR>\n" );
document.write( "time = 30/4 which becomes:<BR>\n" );
document.write( "time = 7.5 days.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "all of this assumes that each person is working at the same rate of 1/30 of the wall per day.<BR>\n" );
document.write( "there is no distinction between the rate that men work and the rate that women work, nor is there any distinction between the rate that individual people who are different from each other work.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );