document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=935391>Question 935391</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Terry the frog and Charles the rabbit want to create a new math course consisting of 30 lessons. If they do the job together, it would take them 300 hours to finish the job. If they do the job separately, Terry would be 60 hours faster than Charles. When they do the job together, how many lessons should Terry expect to do? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #568596 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=568596\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> What is true ( but not exactly stated ) is that each<BR>\n" );
document.write( "one works at a certain rate which doesn't change.<BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "You can call <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+30+ ALIGN=MIDDLE  ALT=\"+30+\"   DISABLED_style= \"max-width:90%; height:auto;\" > lessons <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1+ ALIGN=MIDDLE  ALT=\"+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" > job since they<BR>\n" );
document.write( "are not finished until they have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+30+ ALIGN=MIDDLE  ALT=\"+30+\"   DISABLED_style= \"max-width:90%; height:auto;\" > lessons<BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "Let Charles rate of working be:<BR>\n" );
document.write( "( 1 job ) / ( t hours ) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2Ft+ ALIGN=MIDDLE  ALT=\"+1%2Ft+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------------------<BR>\n" );
document.write( "Terry's rate of working is:<BR>\n" );
document.write( "( 1 job ) / ( t - 60 hrs ) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1+%2F+%28+t-60+%29+ ALIGN=MIDDLE  ALT=\"+1+%2F+%28+t-60+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "since shorter time means faster<BR>\n" );
document.write( "-----------------------------<BR>\n" );
document.write( "If I add their rates of working, I get their<BR>\n" );
document.write( "rate working together<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2Ft+%2B+1%2F%28+t-60+%29+=+1%2F300+ ALIGN=MIDDLE  ALT=\"+1%2Ft+%2B+1%2F%28+t-60+%29+=+1%2F300+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+300t%2A%28+t-60+%29+ ALIGN=MIDDLE  ALT=\"+300t%2A%28+t-60+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+300%2A%28+t-60+%29+%2B+300t+=+t%2A%28+t-60+%29+ ALIGN=MIDDLE  ALT=\"+300%2A%28+t-60+%29+%2B+300t+=+t%2A%28+t-60+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+300t+-+18000+%2B+300t+=+t%5E2+-+60t+ ALIGN=MIDDLE  ALT=\"+300t+-+18000+%2B+300t+=+t%5E2+-+60t+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t%5E2+-+660t+%2B+18000+=+0+ ALIGN=MIDDLE  ALT=\"+t%5E2+-+660t+%2B+18000+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Use the quadratic formula<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+%28+-%28-660%29+%2B-+sqrt%28+%28-660%29%5E2+-+4%2A1%2A18000+%29%29+%2F+%282%2A1%29+ ALIGN=MIDDLE  ALT=\"+t+=+%28+-%28-660%29+%2B-+sqrt%28+%28-660%29%5E2+-+4%2A1%2A18000+%29%29+%2F+%282%2A1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+%28+660+%2B-+sqrt%28+435600+-+72000+%29%29+%2F+2+ ALIGN=MIDDLE  ALT=\"+t+=+%28+660+%2B-+sqrt%28+435600+-+72000+%29%29+%2F+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+%28+660+%2B-+sqrt%28+363600+%29%29+%2F+2+ ALIGN=MIDDLE  ALT=\"+t+=+%28+660+%2B-+sqrt%28+363600+%29%29+%2F+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+%28+660+%2B+603+%29+%2F+2+ ALIGN=MIDDLE  ALT=\"+t+=+%28+660+%2B+603+%29+%2F+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+1263%2F2+ ALIGN=MIDDLE  ALT=\"+t+=+1263%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+631.5+ ALIGN=MIDDLE  ALT=\"+t+=+631.5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+-+60+=+571.5+ ALIGN=MIDDLE  ALT=\"+t+-+60+=+571.5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "check:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2Ft+%2B+1%2F%28+t-60+%29+=+1%2F300+ ALIGN=MIDDLE  ALT=\"+1%2Ft+%2B+1%2F%28+t-60+%29+=+1%2F300+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F631.5+%2B+1%2F571.5+=+1%2F300+ ALIGN=MIDDLE  ALT=\"+1%2F631.5+%2B+1%2F571.5+=+1%2F300+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+.0015835+%2B+.0017497+=+.0033333+ ALIGN=MIDDLE  ALT=\"+.0015835+%2B+.0017497+=+.0033333+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+.0033332+=+.0033333+ ALIGN=MIDDLE  ALT=\"+.0033332+=+.0033333+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "( error due to rounding off )<BR>\n" );
document.write( "--------------------------<BR>\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+ ALIGN=MIDDLE  ALT=\"+x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the fraction of the job<BR>\n" );
document.write( "done by Charles, then:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+ ALIGN=MIDDLE  ALT=\"+x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = ( his rate ) x ( time to finish )<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+300+%2F+631.5+ ALIGN=MIDDLE  ALT=\"+x+=+300+%2F+631.5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+.47506+ ALIGN=MIDDLE  ALT=\"+x+=+.47506+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+.47506%2A30+=+14.25+ ALIGN=MIDDLE  ALT=\"+.47506%2A30+=+14.25+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Charles could finish 14 lessons, so<BR>\n" );
document.write( "Terry could finish <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+30+-+14+ ALIGN=MIDDLE  ALT=\"+30+-+14+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or<BR>\n" );
document.write( "16 lessons<BR>\n" );
document.write( "Hope I got this right\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );