document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=300150>Question 300150</A>: <I><SPAN STYLE=\"word-break: break-all;\"> It takes Jack 9 hours longer to paint the fence than Mike.  Together, they can paint the fence in 20 hours.  How long will it take each person to paint the fence?\r<BR>\n" );
document.write( "\n" );
document.write( "I tried solving this as an inverse work-rate problem using \r<BR>\n" );
document.write( "\n" );
document.write( "1/A + 1/B = 20 but I can't get it to work.   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #215441 by </B><A HREF=/tutors/aboutme.mpl?userid=richwmiller><B>richwmiller(17219)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richwmiller><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=richwmiller><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=215441\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 20/x+20/(x+9)=1<BR>\n" );
document.write( "The one means one job<BR>\n" );
document.write( "We are trying to find what fraction of the job Jack does and what fraction of the job Mike does. Together it has to add up to one whole job or 100% of the job<BR>\n" );
document.write( "20/x is how much Mike does in the4 20 hour job<BR>\n" );
document.write( "20/(x+9) is the part Jack does since he takes longer.<BR>\n" );
document.write( "jack can do it in x+9 hours and so he does 1/(x+9) in one hour.<BR>\n" );
document.write( "in 20/(x+9) he does his part of the 20 hour job\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "so we multiply 20/x by (x+9)/(x+9)<BR>\n" );
document.write( "and we multiply 20/(x+9) by x/x<BR>\n" );
document.write( "(20*(x+9)+20x)/x*(x+9)=1<BR>\n" );
document.write( "(40x+180)=x^2+9x<BR>\n" );
document.write( "0=x^2-31x-180<BR>\n" );
document.write( "we want factors of -180 that add up to -31<BR>\n" );
document.write( "-18 and 10 sum -8<BR>\n" );
document.write( "-36 and 5 -31<BR>\n" );
document.write( "ok<BR>\n" );
document.write( "(x-36)*(x+5)=0<BR>\n" );
document.write( "x=36 and x=-5<BR>\n" );
document.write( "reject negative<BR>\n" );
document.write( "x=36<BR>\n" );
document.write( "20/36+20/45=1<BR>\n" );
document.write( "5/9+4/9=1<BR>\n" );
document.write( "jack take 45 hours alone and mike takes 36 alone<BR>\n" );
document.write( "and together they take 20 hours<BR>\n" );
document.write( "in 20 hours jack does 4/9 of the job and mike does 5/9<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );