document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=485104>Question 485104</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have a story problem I can't figure out. Can you help me and show me the steps to solve it? Thanks you. The speed of a moving walkway is about 4.5 feet per second. Walking on the moving walkway, it takes Karen a total of 20 seconds to travel 45 feet with the movement of the walkway and then back again against the movement of the walkway. What is Karen's normal walking speed?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #331839 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=331839\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The speed of a moving walkway is about 4.5 feet per second. <BR>\n" );
document.write( "Walking on the moving walkway, it takes Karen a total of 20 seconds to travel 45<BR>\n" );
document.write( " feet with the movement of the walkway and then back again against the movement of the walkway.<BR>\n" );
document.write( " What is Karen's normal walking speed? <BR>\n" );
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document.write( "Let x = K's normal walking speed in ft/sec<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(x+4.5) = K's speed going the same as the walkway<BR>\n" );
document.write( "and<BR>\n" );
document.write( "(x-4.5) = K's speed going against the walkway<BR>\n" );
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document.write( "Write a time equation: time = dist/speed<BR>\n" );
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document.write( "with time + against time = 20 sec<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45%2F%28x%2B4.5%29 ALIGN=MIDDLE  ALT=\"45%2F%28x%2B4.5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45%2F%28x-4.5%29 ALIGN=MIDDLE  ALT=\"45%2F%28x-4.5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 20<BR>\n" );
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document.write( "Multiply by (x+4.5)(x-4.5)<BR>\n" );
document.write( "(x+4.5)(x-4.5)*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45%2F%28x%2B4.5%29 ALIGN=MIDDLE  ALT=\"45%2F%28x%2B4.5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + (x+4.5)(x-4.5)*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45%2F%28x-4.5%29 ALIGN=MIDDLE  ALT=\"45%2F%28x-4.5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 20(x+4.5)(x-4.5)<BR>\n" );
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document.write( "Cancel the denominators FOIL the right side and you have:<BR>\n" );
document.write( "45(x-4.5) + 45(x+4.5) = 20(x^2 - 4.5x + 4.5x - 20.25)<BR>\n" );
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document.write( "45x - 202.5 + 45x + 202.5 = 20(x^2 - 20.25)<BR>\n" );
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document.write( "90x = 20x^2 - 405<BR>\n" );
document.write( "A quadratic equation<BR>\n" );
document.write( "20x^2 - 90x - 405 = 0<BR>\n" );
document.write( "Simplify, divide by 5<BR>\n" );
document.write( "4x^2 - 18x - 81 = 0<BR>\n" );
document.write( "Use the quadratic formula to find x<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%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( "a=4; b=-18; c=-81<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%28-18%29+%2B-+sqrt%28-18%5E2-4%2A4%2A-81+%29%29%2F%282%2A4%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-%28-18%29+%2B-+sqrt%28-18%5E2-4%2A4%2A-81+%29%29%2F%282%2A4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2818+%2B-+sqrt%28324-%28-1296%29+%29%29%2F%288%29+ ALIGN=MIDDLE  ALT=\"x+=+%2818+%2B-+sqrt%28324-%28-1296%29+%29%29%2F%288%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2818+%2B-+sqrt%281620+%29%29%2F%288%29+ ALIGN=MIDDLE  ALT=\"x+=+%2818+%2B-+sqrt%281620+%29%29%2F%288%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "we only care about the positive solution here<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2818+%2B+40.25%29%2F%288%29+ ALIGN=MIDDLE  ALT=\"x+=+%2818+%2B+40.25%29%2F%288%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=58.25%2F8 ALIGN=MIDDLE  ALT=\"58.25%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = 7.28 ft/sec is K's normal walking speed<BR>\n" );
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document.write( "You can confirm this by finding the time for each direction:<BR>\n" );
document.write( "45/(7.28+4.5) = 3.82 sec<BR>\n" );
document.write( "45/(7.28-4.5) = 16.18 sec<BR>\n" );
document.write( "---------------------------<BR>\n" );
document.write( "round trip time:20.00 sec<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Did you understand the steps we took here? </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );