document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=924413>Question 924413</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A alone would take 6 hours more to complete the job than if both A and B would work together. When B worked alone he took 1.5 hours more to complete the job and A and B worked together. How much time they will take if they work together? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #560832 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=560832\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  A alone would take 6 hours more to complete the job than if both A and B would work together.<BR>\n" );
document.write( " When B worked alone he took 1.5 hours more to complete the job and A and B worked together.<BR>\n" );
document.write( " How much time they will take if they work together?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "let t = time required when A & B work together<BR>\n" );
document.write( "Let the completed job = 1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%2Fa ALIGN=MIDDLE  ALT=\"t%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%2Fb ALIGN=MIDDLE  ALT=\"t%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( ":<BR>\n" );
document.write( "\" A alone would take 6 hours more to complete the job than if both A and B would work together.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28t%2B6%29%29%2Fa ALIGN=MIDDLE  ALT=\"%28%28t%2B6%29%29%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( "therefore<BR>\n" );
document.write( "a = t+6<BR>\n" );
document.write( "\" When B worked alone he took 1.5 hours more to complete the job and A and B worked together.\"<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28t%2B1.5%29%29%2Fb ALIGN=MIDDLE  ALT=\"%28%28t%2B1.5%29%29%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( "therefore<BR>\n" );
document.write( "b = t+1.5<BR>\n" );
document.write( "Replace a & b in the 1st equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%2F%28%28t%2B6%29%29 ALIGN=MIDDLE  ALT=\"t%2F%28%28t%2B6%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%2F%28%28t%2B1.5%29%29 ALIGN=MIDDLE  ALT=\"t%2F%28%28t%2B1.5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( "multiply the equation by (t+6)(t+1.5), cancel the denominators, we have:<BR>\n" );
document.write( "t(t+1.5) + t(t+6) = (t+6)(t+1.5)<BR>\n" );
document.write( "t^2 + 1.5t + t^2 + 6t = t^2 + 1.5t + 6t + 9<BR>\n" );
document.write( "2t^2 + 7.5t = t^2 + 7.5t = 9<BR>\n" );
document.write( "2t^2 - t^2 + 7.5t - 7.5t = 9<BR>\n" );
document.write( "t^2 = 9<BR>\n" );
document.write( "t = 3 hrs if they work together?<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "We can check this, now we know that a would take 9 hrs alone and b take 4.5 hr<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F9 ALIGN=MIDDLE  ALT=\"3%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F4.5 ALIGN=MIDDLE  ALT=\"3%2F4.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( ".333 + .667 = 1 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );