document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=269393>Question 269393</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Biking into the wind on a flat path, a bicyclist takes 5 hours to travel 30 miles. The return bike takes 3 hours. The wind speed remains constant during the trip.\r<BR>\n" );
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document.write( "a. Find the bicyclist's average speed for each leg of the trip.\r<BR>\n" );
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document.write( "b. Write a system of linear equations that represent the situation. \r<BR>\n" );
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document.write( "c. What is the bicyclist's average speed in still air? What is the speed of the wind? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #197555 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=197555\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w ALIGN=MIDDLE  ALT=\"w\"   DISABLED_style= \"max-width:90%; height:auto;\" > = wind speed<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > = bike's speed with no wind<BR>\n" );
document.write( "The trip that takes less time is with the wind<BR>\n" );
document.write( "The 2 equations to use are:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+%28b+-+w%29%2At%5B1%5D ALIGN=MIDDLE  ALT=\"d+=+%28b+-+w%29%2At%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > (against the wind)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+%28b+%2B+w%29%2At%5B2%5D ALIGN=MIDDLE  ALT=\"d+=+%28b+%2B+w%29%2At%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > (with the wind)<BR>\n" );
document.write( "given:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+30 ALIGN=MIDDLE  ALT=\"d+=+30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B1%5D+=+5 ALIGN=MIDDLE  ALT=\"t%5B1%5D+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" > hrs<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B2%5D+=+3 ALIGN=MIDDLE  ALT=\"t%5B2%5D+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > hrs<BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "The only unknowns are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w ALIGN=MIDDLE  ALT=\"w\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "so I've got 2 equations and 2 unknowns<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30+=+%28b+-+w%29%2A5 ALIGN=MIDDLE  ALT=\"30+=+%28b+-+w%29%2A5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30+=+5b+-+5w ALIGN=MIDDLE  ALT=\"30+=+5b+-+5w\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6+=+b+-+w ALIGN=MIDDLE  ALT=\"6+=+b+-+w\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30+=+%28b+%2B+w%29%2A3 ALIGN=MIDDLE  ALT=\"30+=+%28b+%2B+w%29%2A3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30+=+3b+%2B+3w ALIGN=MIDDLE  ALT=\"30+=+3b+%2B+3w\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10+=+b+%2B+w ALIGN=MIDDLE  ALT=\"10+=+b+%2B+w\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "Add the equations<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10+=+b+%2B+w ALIGN=MIDDLE  ALT=\"10+=+b+%2B+w\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6+=+b+-+w ALIGN=MIDDLE  ALT=\"6+=+b+-+w\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16+=+2b ALIGN=MIDDLE  ALT=\"16+=+2b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+8 ALIGN=MIDDLE  ALT=\"b+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and, since<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10+=+b+%2B+w ALIGN=MIDDLE  ALT=\"10+=+b+%2B+w\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10+=+8+%2B+w ALIGN=MIDDLE  ALT=\"10+=+8+%2B+w\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w+=+2 ALIGN=MIDDLE  ALT=\"w+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------<BR>\n" );
document.write( "(a) <BR>\n" );
document.write( "The bicyclist's average speed for the 1st leg:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+-+w+=+8+-+2 ALIGN=MIDDLE  ALT=\"b+-+w+=+8+-+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+-+w+=+6 ALIGN=MIDDLE  ALT=\"b+-+w+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" > mi/hr<BR>\n" );
document.write( "The bicyclist's average speed for the 2nd leg:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+%2B+w+=+8+%2B+2 ALIGN=MIDDLE  ALT=\"b+%2B+w+=+8+%2B+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+%2B+w+=+10 ALIGN=MIDDLE  ALT=\"b+%2B+w+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" > mi/hr<BR>\n" );
document.write( "----------------------<BR>\n" );
document.write( "(b)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+-+w+=+6 ALIGN=MIDDLE  ALT=\"b+-+w+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+%2B+w+=+10 ALIGN=MIDDLE  ALT=\"b+%2B+w+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "(c)<BR>\n" );
document.write( "In still air the cyclist's speed is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+8 ALIGN=MIDDLE  ALT=\"b+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" > mi/hr<BR>\n" );
document.write( "The wind seed is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w+=+2 ALIGN=MIDDLE  ALT=\"w+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > mi/hr\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );