document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=168173>Question 168173</A>: <I><SPAN STYLE=\"word-break: break-all;\"> It takes Lucy 15 minutes longer to clean her garage alone than it takes her brother Billy.  Together they can clean the garage in 4 minutes.  If Lucy were cleaning the garage alone, how long would it take her to complete 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 #123931 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=123931\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> : <BR>\n" );
document.write( "It takes Lucy 15 minutes longer to clean her garage alone than it takes her brother Billy. <BR>\n" );
document.write( ":<BR>\n" );
document.write( "Together they can clean the garage in 4 minutes. <BR>\n" );
document.write( ":<BR>\n" );
document.write( "If Lucy were cleaning the garage alone, how long would it take her to complete the job?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let x = L's time (in minutes) working alone<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(x-15) = B's time working alone<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let the completed job = 1<BR>\n" );
document.write( ":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F%28%28x-15%29%29 ALIGN=MIDDLE  ALT=\"4%2F%28%28x-15%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Fx ALIGN=MIDDLE  ALT=\"4%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Multiply equation by x(x-15) to get rid of the denominators, results:<BR>\n" );
document.write( "4x + 4(x-15) = x(x-15)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "4x + 4x - 60 = x^2 - 15x<BR>\n" );
document.write( ":<BR>\n" );
document.write( "8x - 60 = x^2 - 15x<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Arrange as a quadratic equation:<BR>\n" );
document.write( "x^2 - 15x - 8x + 60 = 0<BR>\n" );
document.write( ":<BR>\n" );
document.write( "x^2 - 23x + 60 = 0<BR>\n" );
document.write( "Factor this to:<BR>\n" );
document.write( "(x - 3)(x - 20)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "x = 3 does not make sense<BR>\n" );
document.write( ":<BR>\n" );
document.write( "x = 20 min, L's time working alone.<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Check solution; B's time would be 20 - 15 = 5 min<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F5 ALIGN=MIDDLE  ALT=\"4%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F20 ALIGN=MIDDLE  ALT=\"4%2F20\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );