document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=936590>Question 936590</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The number of hours required to do a painting job is represented by the function f(x)=2x , where f(x) gives the number of hours and x is the number of painters doing the job. How much time will {4, 10, 14, 16, 18} workers take to do the job? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #570062 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=570062\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the equation is f(x) = 2x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "based on this equation:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "4 workers will take 8 hours.<BR>\n" );
document.write( "10 workers will take 20 hours.<BR>\n" );
document.write( "14 workers will take 28 hours.<BR>\n" );
document.write( "16 workers will take 32 hours.<BR>\n" );
document.write( "18 workers will take 36 hours.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that's you solution, and you can stop here if you want to.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "otherwise, read on.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this doesn't make sense, since you would think that more workers would take less time to do the same job.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if you assume that f(x) is equal to the overall rate that they work, then it makes more sense.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the formula for work is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "r * p * t = q\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "r is the rate of one person.<BR>\n" );
document.write( "p is the number of persons working at the same rate.<BR>\n" );
document.write( "t is the amount of time to do the job.<BR>\n" );
document.write( "q is the quantity of work.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "in this problem, we would translate the numbers as follows:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2 = rate of one worker.<BR>\n" );
document.write( "x = number of workers.<BR>\n" );
document.write( "t is what we want to find.<BR>\n" );
document.write( "q is 1 job.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the formula of r * p * t = q becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2 * x * t = 1\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "solve for t in this equation to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "t = 1 / (2 * x)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if x = 1, then the job is finished in 1/2 hours.<BR>\n" );
document.write( "if x = 4, then the job is finished in 1/8 of an hour.<BR>\n" );
document.write( "if x = 10, the job is finished in 1/20 of an hour.<BR>\n" );
document.write( "etc.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "bottom line is more workers to do the same job results in less time to do the job assuming they all work at the same rate per worker.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "in real life, there is an optimal number of workers after which the efficiency drops off and the average rate per worker decreases.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );