document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=737108>Question 737108</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The Austin Healthmate 400 can purify the air in a conference hall in 15 fewer minutes than it takes the Airgle 750 Air Purifier to do the same job. Together the two machines can purify the air in the conference hall in 10 minutes. How long would it take each machine, working alone, to purify the air in the room? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #450188 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=450188\">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;\" > = time in minutes for Airgle 750 to do the job<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+-+15+ ALIGN=MIDDLE  ALT=\"+t+-+15+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = time for A. H. 400 to do job<BR>\n" );
document.write( "----------<BR>\n" );
document.write( "Add their rate of purifying:<BR>\n" );
document.write( "( 1 job ) / ( t min ) + ( 1 job ) / ( t - 15 min ) = 1 / 10 min<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2Ft+%2B+1%2F%28+t-15+%29+=+1%2F10+ ALIGN=MIDDLE  ALT=\"+1%2Ft+%2B+1%2F%28+t-15+%29+=+1%2F10+\"   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-15+%29%2A10+ ALIGN=MIDDLE  ALT=\"+t%2A%28+t-15+%29%2A10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+10%2A%28+t-15+%29+%2B+10t+=+t%2A%28+t-15+%29+ ALIGN=MIDDLE  ALT=\"+10%2A%28+t-15+%29+%2B+10t+=+t%2A%28+t-15+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+10t+-+150+%2B+10t+=+t%5E2+-+15t+ ALIGN=MIDDLE  ALT=\"+10t+-+150+%2B+10t+=+t%5E2+-+15t+\"   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+-+35t+%2B+150+=+0+ ALIGN=MIDDLE  ALT=\"+t%5E2+-+35t+%2B+150+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><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+=+-35+ ALIGN=MIDDLE  ALT=\"+b+=+-35+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c+=+150+ ALIGN=MIDDLE  ALT=\"+c+=+150+\"   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+-%28-35%29+%2B-+sqrt%28+%28-35%29%5E2+-+4%2A1%2A150+%29%29+%2F+%282%2A1%29+ ALIGN=MIDDLE  ALT=\"+t+=+%28+-%28-35%29+%2B-+sqrt%28+%28-35%29%5E2+-+4%2A1%2A150+%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+35+%2B-+sqrt%28+1225+-+600+%29%29+%2F+2+ ALIGN=MIDDLE  ALT=\"+t+=+%28+35+%2B-+sqrt%28+1225+-+600+%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+35+%2B+sqrt%28+625+%29%29+%2F+2+ ALIGN=MIDDLE  ALT=\"+t+=+%28+35+%2B+sqrt%28+625+%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+35+%2B+25+%29+%2F+2+ ALIGN=MIDDLE  ALT=\"+t+=+%28+35+%2B+25+%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+=+30+ ALIGN=MIDDLE  ALT=\"+t+=+30+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and, also<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+%28+35+-+25+%29+%2F+2+ ALIGN=MIDDLE  ALT=\"+t+=+%28+35+-+25+%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+=+5+ ALIGN=MIDDLE  ALT=\"+t+=+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( reject this solution )<BR>\n" );
document.write( "---------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+-+15+=+15+ ALIGN=MIDDLE  ALT=\"+t+-+15+=+15+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "It took 30 minutes for Airgle 750 to do the job<BR>\n" );
document.write( "It took 15 minutes for A. H. 400 to do job<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "check answers:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2Ft+%2B+1%2F%28+t-15+%29+=+1%2F10+ ALIGN=MIDDLE  ALT=\"+1%2Ft+%2B+1%2F%28+t-15+%29+=+1%2F10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F30+%2B+1%2F15+=+1%2F10+ ALIGN=MIDDLE  ALT=\"+1%2F30+%2B+1%2F15+=+1%2F10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F30+%2B+2%2F30+=+3%2F30+ ALIGN=MIDDLE  ALT=\"+1%2F30+%2B+2%2F30+=+3%2F30+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3%2F30+=+3%2F30+ ALIGN=MIDDLE  ALT=\"+3%2F30+=+3%2F30+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );