document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=828522>Question 828522</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A jogging park has two identical circular tracks touching each other, and a rectangular track enclosing the two circles. The edges of the rectangles are tangential to the circles. Two friends, A and B, start jogging simultaneously form the point where one of the circular tracks touches the smaller side of the rectangular track. A jogs along the rectangular track, while B jogs along the two circular tracks in a figure of eight. Approximately, how much faster than A does B have to run, so that they take the same time to return to their starting point? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #499372 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=499372\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R ALIGN=MIDDLE  ALT=\"R\"   DISABLED_style= \"max-width:90%; height:auto;\" >= radius of each circle, the rectangle's length and width should be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4R ALIGN=MIDDLE  ALT=\"4R\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2R ALIGN=MIDDLE  ALT=\"2R\"   DISABLED_style= \"max-width:90%; height:auto;\" > respectively.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C200%2C-22%2C22%2C-11%2C11%2C%0D%0Arectangle%28-20%2C-10%2C20%2C10%29%2Ccircle%2810%2C0%2C0.2%29%2C%0D%0Aarrow%2810%2C0%2C20%2C0%29%2Carrow%2820%2C0%2C10%2C0%29%2C%0D%0Alocate%2815%2C0%2CR%29%2C%0D%0Acircle%28-10%2C0%2C10%29%2Ccircle%2810%2C0%2C10%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The perimeter of the rectangle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A%284R%2B2R%29=2%2A6R=12R ALIGN=MIDDLE  ALT=\"2%2A%284R%2B2R%29=2%2A6R=12R\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That is the distance A runs in one lap.<BR>\n" );
document.write( "The circumference of a circle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pi%2AR ALIGN=MIDDLE  ALT=\"2pi%2AR\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and the distance that B runs in one lap is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A%282pi%2AR%29=4pi%2AR ALIGN=MIDDLE  ALT=\"2%2A%282pi%2AR%29=4pi%2AR\"   DISABLED_style= \"max-width:90%; height:auto;\" > , which is longer than <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12R ALIGN=MIDDLE  ALT=\"12R\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "How much longer?<BR>\n" );
document.write( "The difference is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4pi%2AR-12R ALIGN=MIDDLE  ALT=\"4pi%2AR-12R\"   DISABLED_style= \"max-width:90%; height:auto;\" > and as a fraction of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12R ALIGN=MIDDLE  ALT=\"12R\"   DISABLED_style= \"max-width:90%; height:auto;\" > it is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284pi%2AR-12R%29%2F12R=%284pi-12%29%2AR%2F12R=4pi%2F12%2F12=4pi%2F12-12%2F12=pi%2F3-1=about0.047 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >=4.7%<BR>\n" );
document.write( "So B must run 4.7% more distance in the same time.<BR>\n" );
document.write( "B must be 4.7% faster than A.<BR>\n" );
document.write( " </SPAN>\n" );
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