document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=103822>Question 103822</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Connie can type 600 words in 5 minutes less than it takes Katie to type 600 words. If connie types at a rate of 20 words per minute faster than Katie types, find the typing rate of each woman. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #75478 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20056)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><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=Edwin+McCravy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=75478\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font size = 7 color = \"red\"><b><BR>\n" );
document.write( "MATHLOVER'S SOLUTION IS INCORRECT!<BR>\n" );
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document.write( "CORRECT SOLUTION BY EDWIN:</font><BR>\n" );
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document.write( "Connie can type 600 words in 5 minutes less than it takes Katie to type 600<BR>\n" );
document.write( "words. If connie types at a rate of 20 words per minute faster than Katie<BR>\n" );
document.write( "types, find the typing rate of each woman.<BR>\n" );
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document.write( "Suppose it takes Katie K minutes to type 600 words.<BR>\n" );
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document.write( "Then Katie's rate = (600 words)/(K minutes) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=600%2FK ALIGN=MIDDLE  ALT=\"600%2FK\"   DISABLED_style= \"max-width:90%; height:auto;\" > words/minute.<BR>\n" );
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document.write( "Then from this sentence:<BR>\n" );
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document.write( ">>...Connie can type 600 words in 5 minutes less than it takes Katie to type<BR>\n" );
document.write( "600 words...<<<BR>\n" );
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document.write( "Connie's time to type 600 words is K-5 minutes.<BR>\n" );
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document.write( "Then Connie's rate = (600 words)/(K-5 minutes) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=600%2F%28K-5%29 ALIGN=MIDDLE  ALT=\"600%2F%28K-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > words/minute.<BR>\n" );
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document.write( "Then from this sentences:<BR>\n" );
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document.write( ">>...connie types at a rate of 20 words per minute faster than Katie<BR>\n" );
document.write( "types...<<<BR>\n" );
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document.write( "we form our equation:<BR>\n" );
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document.write( "Connie's rate = Katie's rate + 20 words/minute.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=600%2F%28K-5%29 ALIGN=MIDDLE  ALT=\"600%2F%28K-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=600%2FK ALIGN=MIDDLE  ALT=\"600%2FK\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20 ALIGN=MIDDLE  ALT=\"20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Solve that by first multiplying thru by LCD of K(K-5)<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=K%28K-5%29 ALIGN=MIDDLE  ALT=\"K%28K-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=600%2F%28K-5%29 ALIGN=MIDDLE  ALT=\"600%2F%28K-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=K%28K-5%29 ALIGN=MIDDLE  ALT=\"K%28K-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=600%2FK ALIGN=MIDDLE  ALT=\"600%2FK\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=K%28K-5%29 ALIGN=MIDDLE  ALT=\"K%28K-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20 ALIGN=MIDDLE  ALT=\"20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=600K ALIGN=MIDDLE  ALT=\"600K\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=600%28K-5%29 ALIGN=MIDDLE  ALT=\"600%28K-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20K%28K-5%29 ALIGN=MIDDLE  ALT=\"20K%28K-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=600K ALIGN=MIDDLE  ALT=\"600K\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=600K ALIGN=MIDDLE  ALT=\"600K\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3000 ALIGN=MIDDLE  ALT=\"3000\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20K%5E2 ALIGN=MIDDLE  ALT=\"20K%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100K ALIGN=MIDDLE  ALT=\"100K\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20K%5E2 ALIGN=MIDDLE  ALT=\"20K%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100K ALIGN=MIDDLE  ALT=\"100K\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3000 ALIGN=MIDDLE  ALT=\"3000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Divide every term on both sides by 20:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%2F20 ALIGN=MIDDLE  ALT=\"0%2F20\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2820K%5E2%29%2F20 ALIGN=MIDDLE  ALT=\"%2820K%5E2%29%2F20\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28100K%29%2F20 ALIGN=MIDDLE  ALT=\"%28100K%29%2F20\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3000%2F20 ALIGN=MIDDLE  ALT=\"3000%2F20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=K%5E2 ALIGN=MIDDLE  ALT=\"K%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5K ALIGN=MIDDLE  ALT=\"5K\"   DISABLED_style= \"max-width:90%; height:auto;\" > - 150<BR>\n" );
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document.write( "Factoring:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28K-15%29%28K%2B10%29 ALIGN=MIDDLE  ALT=\"%28K-15%29%28K%2B10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Setting the first factor = 0, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=K-15=0 ALIGN=MIDDLE  ALT=\"K-15=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=K=15 ALIGN=MIDDLE  ALT=\"K=15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Setting the second factor = 0, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=K%2B10=0 ALIGN=MIDDLE  ALT=\"K%2B10=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=K=-10 ALIGN=MIDDLE  ALT=\"K=-10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Discarding the negative answer, Katie's time for typing 600<BR>\n" );
document.write( "word is 15 minutes, so<BR>\n" );
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document.write( "Katie's rate is (600 words)/(15 minutes) = 600/15 words/minute <BR>\n" );
document.write( "or 40 words/minute<BR>\n" );
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document.write( "Connie's time for typing 600 words is 5 minutes less than<BR>\n" );
document.write( "Katie's time for typing 600 words, so her time is 15-5 or 10<BR>\n" );
document.write( "minutes, so<BR>\n" );
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document.write( "Connie's rate is (600 words)/(10 minutes) = 600/10 words/minute<BR>\n" );
document.write( "of 60 words/minute.  <BR>\n" );
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document.write( "This checks with <BR>\n" );
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document.write( ">>...connie types at a rate of 20 words per minute faster than Katie<BR>\n" );
document.write( "types...<< <BR>\n" );
document.write( "` <BR>\n" );
document.write( "Edwin<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );