document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1109352>Question 1109352</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Henry and Harriet are running around an oval that has a perimeter of 400m. Henry takes two and a half minutes to run a full lap while Harriet takes two minutes to run a full lap. If they both start at the same time and run in the same direction, how long will it take Harriet to lap Henry? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #724340 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=724340\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Henry's speed is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=400m%2F%222.5+minutes%22=160 ALIGN=MIDDLE  ALT=\"400m%2F%222.5+minutes%22=160\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%2Fminute ALIGN=MIDDLE  ALT=\"m%2Fminute\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Harriet's speed is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=400m%2F%222+minutes%22=200 ALIGN=MIDDLE  ALT=\"400m%2F%222+minutes%22=200\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%2Fminute ALIGN=MIDDLE  ALT=\"m%2Fminute\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > minutes Henry will have run <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=160x ALIGN=MIDDLE  ALT=\"160x\"   DISABLED_style= \"max-width:90%; height:auto;\" > meters,<BR>\n" );
document.write( "and Harriet will have run <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200x ALIGN=MIDDLE  ALT=\"200x\"   DISABLED_style= \"max-width:90%; height:auto;\" > meters.<BR>\n" );
document.write( "When Harriet laps Henry,<BR>\n" );
document.write( "she will have run <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=400m ALIGN=MIDDLE  ALT=\"400m\"   DISABLED_style= \"max-width:90%; height:auto;\" > (one full lap) longer than Henry.<BR>\n" );
document.write( "That translates as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200x=160x%2B400 ALIGN=MIDDLE  ALT=\"200x=160x%2B400\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Solving that equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200x=160x%2B400 ALIGN=MIDDLE  ALT=\"200x=160x%2B400\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200x-160x=400 ALIGN=MIDDLE  ALT=\"200x-160x=400\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40x=400 ALIGN=MIDDLE  ALT=\"40x=400\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=400%2F40 ALIGN=MIDDLE  ALT=\"x=400%2F40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=10 ALIGN=MIDDLE  ALT=\"x=10\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "It seems to be that Harriet will lap Henry after <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2810+minutes%29 ALIGN=MIDDLE  ALT=\"highlight%2810+minutes%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Let's verify.<BR>\n" );
document.write( "In 10 minutes Harry will have run <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4laps=10minutes%2F%222.5+minutes%22 ALIGN=MIDDLE  ALT=\"4laps=10minutes%2F%222.5+minutes%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and Harrriet will have run <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5laps=10minutes%2F%222+minutes%22 ALIGN=MIDDLE  ALT=\"5laps=10minutes%2F%222+minutes%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "NOTE: We did not need to know the size of the track, because we could have measure their speeds in laps per minute instead of meters per minute.<BR>\n" );
document.write( "For this particular problems, we could also have figured out the answer by listing how long it took for Henry and for Harriet to run 1, 2, 3, 4, 5, ... laps.<BR>\n" );
document.write( "For Henry:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%282%2C7%2Claps%2C1%2C2%2C3%2C4%2C5%2C%22...%22%2C%0D%0Aminutes%2C2.5%2C5%2C7.5%2C10%2C12.5%2C%22...%22%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "For Harriet:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%282%2C7%2Claps%2C1%2C2%2C3%2C4%2C5%2C%22...%22%2C%0D%0Aminutes%2C2%2C4%2C6%2C8%2C10%2C%22...%22%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "It would not have been so easy, if Harriet had lapped Henry after 4.3 laps for Henry and 5.3 laps for Harriet. </SPAN>\n" );
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