document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=908450>Question 908450</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two people can solve a problem in 20 minutes. One of them<BR>\n" );
document.write( "alone can solve that problem in 9 minutes less than the time<BR>\n" );
document.write( "needed by the second person, how long would it take the<BR>\n" );
document.write( "faster person working alone to solve the problem? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #551034 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=551034\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1/x+1/(x+9)=1/20<BR>\n" );
document.write( "(20*x*(x+9))/x+(20*x*(x+9))/(x+9)=(20*x*(x+9))/20<BR>\n" );
document.write( "(20*(x+9))+20*x=x*(x+9)<BR>\n" );
document.write( "20*x+180+20*x=x^2+9*x<BR>\n" );
document.write( "40*x+180=x^2+9*x<BR>\n" );
document.write( "x^2-31*x-180=0<BR>\n" );
document.write( "Can it be factored?<BR>\n" );
document.write( "What factors of -180 add up to -31?<BR>\n" );
document.write( "Nevertheless, we will complete the square<BR>\n" );
document.write( "x^2-31*x=180<BR>\n" );
document.write( "add it<BR>\n" );
document.write( "x^2-31*x+(-31/2)=180+(-31/2)<BR>\n" );
document.write( "square it<BR>\n" );
document.write( "x^2-31*x+(961/4)=180+(961/4)<BR>\n" );
document.write( "x^2-31*x+(240.25)=180+(240.25)<BR>\n" );
document.write( "x^2-31*x+(240.25)=420.25<BR>\n" );
document.write( "(x-15.5)^2=420.25<BR>\n" );
document.write( "(x-15.5)^2=420.25<BR>\n" );
document.write( "we can continue<BR>\n" );
document.write( "x-15.5=+-20.5<BR>\n" );
document.write( "x=15.5+-20.5<BR>\n" );
document.write( "Positive useful answer:<BR>\n" );
document.write( "x=15.5+20.5<BR>\n" );
document.write( "One answer is x=36<BR>\n" );
document.write( "x+9=9+36<BR>\n" );
document.write( "x+9=45<BR>\n" );
document.write( "check<BR>\n" );
document.write( "1/x+1/(x+9)=1/20<BR>\n" );
document.write( "1/36+1/(36+9)=1/20<BR>\n" );
document.write( "1/36+1/45=1/20<BR>\n" );
document.write( "45/1620+36/1620=1/x<BR>\n" );
document.write( "0.05=0.05<BR>\n" );
document.write( "ok\r<BR>\n" );
document.write( "\n" );
document.write( "Negative useless answer:<BR>\n" );
document.write( "x=15.5-20.5<BR>\n" );
document.write( "Negative answer is x=-5.0<BR>\n" );
document.write( "For real life cases involving time, distance and other measurements, we reject the negative results\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );