document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=698103>Question 698103</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A and B working together can complete a job in 7 1/2 hours. Working alone, A takes 8 hours longer than B to do the job. How long would it take each working alone? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #430517 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=430517\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A and B working together can complete a job in 7 1/2 hours.<BR>\n" );
document.write( " Working alone, A takes 8 hours longer than B to do the job.<BR>\n" );
document.write( " How long would it take each working alone<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let b = B's time working alone<BR>\n" );
document.write( "A takes 8 hrs longer, therefore<BR>\n" );
document.write( "(b+8) = A's time alone<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=7.5%2Fb ALIGN=MIDDLE  ALT=\"7.5%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7.5%2F%28%28b%2B8%29%29 ALIGN=MIDDLE  ALT=\"7.5%2F%28%28b%2B8%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( "multiply by b(b+8), resulting in:<BR>\n" );
document.write( "7.5(b+8) + 7.5b = b(b+8)<BR>\n" );
document.write( "7.5b + 60 + 7.5b = b^2 + 8b<BR>\n" );
document.write( "A quadratic equation<BR>\n" );
document.write( "0 = b^2 + 8b - 15b - 60<BR>\n" );
document.write( "b^2 - 7b - 60 = 0<BR>\n" );
document.write( "Factors to<BR>\n" );
document.write( "(b-12)(b+5) = 0<BR>\n" );
document.write( "the positive solution<BR>\n" );
document.write( "b = 12 hours, B working alone<BR>\n" );
document.write( "then<BR>\n" );
document.write( "12 + 8 = 20 hrs A working alone<BR>\n" );
document.write( ":\"<BR>\n" );
document.write( ":<BR>\n" );
document.write( "See it that checks out<BR>\n" );
document.write( "7.5/12 + 7.5/20 =<BR>\n" );
document.write( ".625 + .375 = 1; confirms our solutions </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );