document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=177422>Question 177422</A>: <I><SPAN STYLE=\"word-break: break-all;\"> It took Emily 25 min to ride her bike to the repair shop and 1h 15 min to walk back home. If she can ride her bike 8km/h faster than she can walk, how far is the repair shop from her house. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #132471 by </B><A HREF=/tutors/aboutme.mpl?userid=Electrified_Levi><B>Electrified_Levi(103)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Electrified_Levi><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=132471\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi, Hope I can help,<BR>\n" );
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document.write( "It took Emily 25 min to ride her bike to the repair shop and 1h 15 min to walk back home. If she can ride her bike 8km/h faster than she can walk, how far is the repair shop from her house.<BR>\n" );
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document.write( "To find the answer we need to know a formula<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+distance+=+%28rate%29%28time%29+ ALIGN=MIDDLE  ALT=\"+distance+=+%28rate%29%28time%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "We can also say <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28rate%29%28time%29+=+%28rate%29%28time%29+ ALIGN=MIDDLE  ALT=\"+%28rate%29%28time%29+=+%28rate%29%28time%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, Emily went on her bike for a distance, and she went back to her home, the same distance<BR>\n" );
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document.write( "We don't know how fast it takes Emily to walk, so we will say she walks \"x\" km/h<BR>\n" );
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document.write( "She can ride her bike 8 km/h fast than she can walk, so she goes \" x + 8 \" km/h on her bike<BR>\n" );
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document.write( "It takes 25 minutes or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5%2F12+ ALIGN=MIDDLE  ALT=\"+5%2F12+\"   DISABLED_style= \"max-width:90%; height:auto;\" > hour ( it has to be the same measurement as the rate ) to ride her bike to the repair shop<BR>\n" );
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document.write( "It takes her 1hour 15 minutes, or 1 <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F4+ ALIGN=MIDDLE  ALT=\"+1%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > hour to walk back home<BR>\n" );
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document.write( "The rate of her on the bike multiplied by the time it takes on the bike will equal the rate of her walking multiplied by the time it takes her to walk<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28rate%29%28time%29+=+%28rate%29%28time%29+ ALIGN=MIDDLE  ALT=\"+%28rate%29%28time%29+=+%28rate%29%28time%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28rate-on-bike%29%28time-on-bike%29+=+%28rate-walking%29%28time-walking%29+ ALIGN=MIDDLE  ALT=\"+%28rate-on-bike%29%28time-on-bike%29+=+%28rate-walking%29%28time-walking%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now replace all the unknowns with what we know<BR>\n" );
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document.write( "rate on bike = (x + 8) km/hr<BR>\n" );
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document.write( "time on bike = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5%2F12+ ALIGN=MIDDLE  ALT=\"+5%2F12+\"   DISABLED_style= \"max-width:90%; height:auto;\" > hour<BR>\n" );
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document.write( "rate walking = x km/hr<BR>\n" );
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document.write( "time walking = 1 <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F4+ ALIGN=MIDDLE  ALT=\"+1%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > hours or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5%2F4+ ALIGN=MIDDLE  ALT=\"+5%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > hours<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28rate-on-bike%29%28time-on-bike%29+=+%28rate-walking%29%28time-walking%29+ ALIGN=MIDDLE  ALT=\"+%28rate-on-bike%29%28time-on-bike%29+=+%28rate-walking%29%28time-walking%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x+%2B+8%29%285%2F12%29+=+%28x%29%285%2F4%29+ ALIGN=MIDDLE  ALT=\"+%28x+%2B+8%29%285%2F12%29+=+%28x%29%285%2F4%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=+%28x+%2B+8%29%285%2F12%29+=+%28x%29%285%2F4%29+ ALIGN=MIDDLE  ALT=\"+%28x+%2B+8%29%285%2F12%29+=+%28x%29%285%2F4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, now we will multiply the numbers out<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x+%2B+8%29%285%2F12%29+=+%28x%29%285%2F4%29+ ALIGN=MIDDLE  ALT=\"+%28x+%2B+8%29%285%2F12%29+=+%28x%29%285%2F4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x+%2B+8%29%285%2F12%29+=+%28x%2F1%29%285%2F4%29+ ALIGN=MIDDLE  ALT=\"+%28x+%2B+8%29%285%2F12%29+=+%28x%2F1%29%285%2F4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x+%2B+8%29%285%2F12%29+=+5x%2F4+ ALIGN=MIDDLE  ALT=\"+%28x+%2B+8%29%285%2F12%29+=+5x%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we will rearrange the left side<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x+%2B+8%29%285%2F12%29+=+5x%2F4+ ALIGN=MIDDLE  ALT=\"+%28x+%2B+8%29%285%2F12%29+=+5x%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%285%2F12%29%28x+%2B+8%29+=+5x%2F4+ ALIGN=MIDDLE  ALT=\"+%285%2F12%29%28x+%2B+8%29+=+5x%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%285%2F12%29%28%28x%2F1%29+%2B+%288%2F1%29%29+=+5x%2F4+ ALIGN=MIDDLE  ALT=\"+%285%2F12%29%28%28x%2F1%29+%2B+%288%2F1%29%29+=+5x%2F4+\"   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=+%285%2F12%29%28%28x%2F1%29+%2B+%288%2F1%29%29+=+5x%2F4+ ALIGN=MIDDLE  ALT=\"+%285%2F12%29%28%28x%2F1%29+%2B+%288%2F1%29%29+=+5x%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we will use the distribution method to multiply the left side out<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%285%2F12%29%28%28x%2F1%29+%2B+%288%2F1%29%29+=+5x%2F4+ ALIGN=MIDDLE  ALT=\"+%285%2F12%29%28%28x%2F1%29+%2B+%288%2F1%29%29+=+5x%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+highlight%285%2F12%29%28highlight%28x%2F1%29+%2B+%288%2F1%29%29+=+5x%2F4+ ALIGN=MIDDLE  ALT=\"+highlight%285%2F12%29%28highlight%28x%2F1%29+%2B+%288%2F1%29%29+=+5x%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+highlight%285%2F12%29%28%28x%2F1%29+%2B+highlight%288%2F1%29%29+=+5x%2F4+ ALIGN=MIDDLE  ALT=\"+highlight%285%2F12%29%28%28x%2F1%29+%2B+highlight%288%2F1%29%29+=+5x%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%285%2F12%29%28x%2F1%29+%2B+%285%2F12%29%288%2F1%29+=+5x%2F4+ ALIGN=MIDDLE  ALT=\"+%285%2F12%29%28x%2F1%29+%2B+%285%2F12%29%288%2F1%29+=+5x%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%285x%2F12%29+%2B+%2840%2F12%29+=+5x%2F4+ ALIGN=MIDDLE  ALT=\"+%285x%2F12%29+%2B+%2840%2F12%29+=+5x%2F4+\"   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=+%285x%2F12%29+%2B+%2840%2F12%29+=+5x%2F4+ ALIGN=MIDDLE  ALT=\"+%285x%2F12%29+%2B+%2840%2F12%29+=+5x%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, to get rid of the fractions we will multiply each side by \"12\"<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%285x%2F12%29+%2B+%2840%2F12%29+=+5x%2F4+ ALIGN=MIDDLE  ALT=\"+%285x%2F12%29+%2B+%2840%2F12%29+=+5x%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+12%28%285x%2F12%29+%2B+%2840%2F12%29%29+=+12%285x%2F4%29+ ALIGN=MIDDLE  ALT=\"+12%28%285x%2F12%29+%2B+%2840%2F12%29%29+=+12%285x%2F4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > =<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+12%28%285x%2F12%29+%2B+%2840%2F12%29%29+=+15x+ ALIGN=MIDDLE  ALT=\"+12%28%285x%2F12%29+%2B+%2840%2F12%29%29+=+15x+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now we will use distribution<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+12%28%285x%2F12%29+%2B+%2840%2F12%29%29+=+15x+ ALIGN=MIDDLE  ALT=\"+12%28%285x%2F12%29+%2B+%2840%2F12%29%29+=+15x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+highlight%2812%29%28highlight%285x%2F12%29+%2B+%2840%2F12%29%29+=+15x+ ALIGN=MIDDLE  ALT=\"+highlight%2812%29%28highlight%285x%2F12%29+%2B+%2840%2F12%29%29+=+15x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+highlight%2812%29%28%285x%2F12%29+%2B+highlight%2840%2F12%29%29+=+15x+ ALIGN=MIDDLE  ALT=\"+highlight%2812%29%28%285x%2F12%29+%2B+highlight%2840%2F12%29%29+=+15x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+12%285x%2F12%29+%2B+12%2840%2F12%29+=+15x+ ALIGN=MIDDLE  ALT=\"+12%285x%2F12%29+%2B+12%2840%2F12%29+=+15x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5x+%2B+40+=+15x+ ALIGN=MIDDLE  ALT=\"+5x+%2B+40+=+15x+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, now we will move \"5x\" to the right side<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5x+%2B+40+=+15x+ ALIGN=MIDDLE  ALT=\"+5x+%2B+40+=+15x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5x+-+5x+%2B+40+=+15x+-+5x+ ALIGN=MIDDLE  ALT=\"+5x+-+5x+%2B+40+=+15x+-+5x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+40+=+10x+ ALIGN=MIDDLE  ALT=\"+40+=+10x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+10x+=+40+ ALIGN=MIDDLE  ALT=\"+10x+=+40+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "to find \"x\" we will divide each side by \"10\"<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+10x+=+40+ ALIGN=MIDDLE  ALT=\"+10x+=+40+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+10x%2F10+=+40%2F10+ ALIGN=MIDDLE  ALT=\"+10x%2F10+=+40%2F10+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+40%2F10+ ALIGN=MIDDLE  ALT=\"+x+=+40%2F10+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+4+ ALIGN=MIDDLE  ALT=\"+x+=+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "We found \"x\"<BR>\n" );
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document.write( "We can check by replacing \"x\" with \"4\" in our original equation<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x+%2B+8%29%285%2F12%29+=+%28x%29%285%2F4%29+ ALIGN=MIDDLE  ALT=\"+%28x+%2B+8%29%285%2F12%29+=+%28x%29%285%2F4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28%284%29+%2B+8%29%285%2F12%29+=+%284%29%285%2F4%29+ ALIGN=MIDDLE  ALT=\"+%28%284%29+%2B+8%29%285%2F12%29+=+%284%29%285%2F4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%2812%29%285%2F12%29+=+%284%29%285%2F4%29+ ALIGN=MIDDLE  ALT=\"+%2812%29%285%2F12%29+=+%284%29%285%2F4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The denominators cross out<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+cross%2812%29%285%2Fcross%2812%29%29+=+cross%284%29%285%2Fcross%284%29%29+ ALIGN=MIDDLE  ALT=\"+cross%2812%29%285%2Fcross%2812%29%29+=+cross%284%29%285%2Fcross%284%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5+=+5+ ALIGN=MIDDLE  ALT=\"+5+=+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" > (True)<BR>\n" );
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document.write( "rate walking = x km/hr, we can replace \"x\" with \"4\"<BR>\n" );
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document.write( "rate walking = 4 km/hr<BR>\n" );
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document.write( "rate on bike = (x + 8) km/hr, replace \"x\" with \"4\"<BR>\n" );
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document.write( "rate on bike = (4 + 8) km/hr<BR>\n" );
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document.write( "rate on bike = 12 km/hr<BR>\n" );
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document.write( "rate on bike = 12 km/hr<BR>\n" );
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document.write( "time on bike = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5%2F12+ ALIGN=MIDDLE  ALT=\"+5%2F12+\"   DISABLED_style= \"max-width:90%; height:auto;\" > hour<BR>\n" );
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document.write( "rate walking = 4 km/hr<BR>\n" );
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document.write( "time walking = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5%2F4+ ALIGN=MIDDLE  ALT=\"+5%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > hours<BR>\n" );
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document.write( "We can now solve for our answer, since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+rate%28time%29+=+distance+ ALIGN=MIDDLE  ALT=\"+rate%28time%29+=+distance+\"   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=+%28rate-on-bike%29%28time-on-bike%29+=+%28rate-walking%29%28time-walking%29+ ALIGN=MIDDLE  ALT=\"+%28rate-on-bike%29%28time-on-bike%29+=+%28rate-walking%29%28time-walking%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%2812%29%285%2F12%29+=+%284%29%285%2F4%29+ ALIGN=MIDDLE  ALT=\"+%2812%29%285%2F12%29+=+%284%29%285%2F4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The denominators cross out<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+cross%2812%29%285%2Fcross%2812%29%29+=+cross%284%29%285%2Fcross%284%29%29+ ALIGN=MIDDLE  ALT=\"+cross%2812%29%285%2Fcross%2812%29%29+=+cross%284%29%285%2Fcross%284%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5+=+5+ ALIGN=MIDDLE  ALT=\"+5+=+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This means that the distance is 5 km, (since that is the measurement)<BR>\n" );
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document.write( "Your answer is 5 km<BR>\n" );
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document.write( "Hope I helped, Levi </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );