document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=945299>Question 945299</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Pat and Jen volunteer at the library. Pat can shelve a full cart of books 14 minutes faster than Jen. If they work together, they can shelve a full cart in 24 minutes. How long does it take Jen to shelve a full cart by herself? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #576658 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=576658\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+ ALIGN=MIDDLE  ALT=\"+t+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = Jen's time in minutes to shelve a cart<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+-+14+ ALIGN=MIDDLE  ALT=\"+t+-+14+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = Pat's time in minutes to shelve a cart<BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "Jen's rate:<BR>\n" );
document.write( "( 1 cart ) / ( t min )<BR>\n" );
document.write( "Pat's rate:<BR>\n" );
document.write( "( 1 cart ) / ( t - 14 min )<BR>\n" );
document.write( "Working together:<BR>\n" );
document.write( "( 1 cart ) / ( 24 min )<BR>\n" );
document.write( "----------------------<BR>\n" );
document.write( "Add their rates to get 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+-+14+%29+=+1%2F24+ ALIGN=MIDDLE  ALT=\"+1%2Ft+%2B+1%2F%28+t+-+14+%29+=+1%2F24+\"   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=+t%2A%28+t+-+14+%29%2A24+ ALIGN=MIDDLE  ALT=\"+t%2A%28+t+-+14+%29%2A24+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+24%2A%28+t+-+14+%29+%2B+24t+=+t%2A%28+t+-+14+%29+ ALIGN=MIDDLE  ALT=\"+24%2A%28+t+-+14+%29+%2B+24t+=+t%2A%28+t+-+14+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+24t+-+336+%2B+24t+=+t%5E2+-+14t+ ALIGN=MIDDLE  ALT=\"+24t+-+336+%2B+24t+=+t%5E2+-+14t+\"   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+-+62t+%2B+336+ ALIGN=MIDDLE  ALT=\"+t%5E2+-+62t+%2B+336+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "Use quadratic formula<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"+t+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+1+ ALIGN=MIDDLE  ALT=\"+a+=+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+-62+ ALIGN=MIDDLE  ALT=\"+b+=+-62+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c+=+336+ ALIGN=MIDDLE  ALT=\"+c+=+336+\"   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+-%28-62%29+%2B-+sqrt%28+%28-62%29%5E2+-+4%2A1%2A336+%29%29+%2F+%282%2A1%29+ ALIGN=MIDDLE  ALT=\"+t+=+%28+-%28-62%29+%2B-+sqrt%28+%28-62%29%5E2+-+4%2A1%2A336+%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+62+%2B-+sqrt%28+3844+-+1344+%29%29+%2F+2+ ALIGN=MIDDLE  ALT=\"+t+=+%28+62+%2B-+sqrt%28+3844+-+1344+%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+62+%2B-+sqrt%28+2500+%29%29+%2F+2+ ALIGN=MIDDLE  ALT=\"+t+=+%28+62+%2B-+sqrt%28+2500+%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+62-+50+%29+%2F+2+ ALIGN=MIDDLE  ALT=\"+t+=+%28+62-+50+%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+=+6+ ALIGN=MIDDLE  ALT=\"+t+=+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "( this answer makes no sense, because it is faster than<BR>\n" );
document.write( "their time working together- 24 min )<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+%28+62+%2B+50+%29+%2F+2+ ALIGN=MIDDLE  ALT=\"+t+=+%28+62+%2B+50+%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+=+112%2F2+ ALIGN=MIDDLE  ALT=\"+t+=+112%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+=+56+ ALIGN=MIDDLE  ALT=\"+t+=+56+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "Working alone, Jen's time is 56 sec<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+-+14+%29+=+1%2F24+ ALIGN=MIDDLE  ALT=\"+1%2Ft+%2B+1%2F%28+t+-+14+%29+=+1%2F24+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F56+%2B+1%2F42+=+1%2F24+ ALIGN=MIDDLE  ALT=\"+1%2F56+%2B+1%2F42+=+1%2F24+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F28+%2B+1%2F21+=+1%2F12+ ALIGN=MIDDLE  ALT=\"+1%2F28+%2B+1%2F21+=+1%2F12+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+252%2F7056+%2B+336%2F7056+=+588%2F7056+ ALIGN=MIDDLE  ALT=\"+252%2F7056+%2B+336%2F7056+=+588%2F7056+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+588+=+588+ ALIGN=MIDDLE  ALT=\"+588+=+588+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );