document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=733323>Question 733323</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am responsible for defending two bicycle cyclists who have been accused of “speeding.” I<BR>\n" );
document.write( "say “speeding” because in one of these towns the law is quite peculiar. A tram runs from the valley of East<BR>\n" );
document.write( "Gausston to the city center of Eulerberg. The travel time from the valley to the city is 40 minutes and a tram<BR>\n" );
document.write( "leaves on the hour every hour between 8 a.m. and 3 p.m. The law here states that no vehicles (including<BR>\n" );
document.write( "bicycles) can make the trip from East Gausston to Eulerberg in less time than it takes the tram. (Some<BR>\n" );
document.write( "suspect that the city council is acting to protect the &#64257;nancial interests of Big Tram). These are the facts<BR>\n" );
document.write( "of the case: My client was invited to Eulerberg to receive an award for her community service e&#64256;orts. She<BR>\n" );
document.write( "left her home in East Gausston in the afternoon on her bicycle. Her bicycle is equipped with a speedometer.<BR>\n" );
document.write( "For the &#64257;rst 5 km she travelled on constant rate of 25 km/hour, then she came to a hill where her speed<BR>\n" );
document.write( "immediately dropped to a constant rate of 15 km/hour as she climbed the 5 km hill. After she reached the<BR>\n" );
document.write( "top she was able to ride at a constant rate of 35 km/hour for the &#64257;nal 5 km to the city center. During her<BR>\n" );
document.write( "acceptance speech she showed the group the readings from her speedometer to illustrate that bicycling is a<BR>\n" );
document.write( "fantastic alternative to driving. After the party she was ticketed for speeding by a local o&#64259;cial. He asserts<BR>\n" );
document.write( "that her average speed was 25 km/hour (averaging her three speeds) and therefore, that it must have taken<BR>\n" );
document.write( "her 36 minutes to traverse the 15 km from her house to the city center. Since this is less than the 40 minutes<BR>\n" );
document.write( "the tram takes, she is guilty of speeding. My client says that the trip actually took just over 40 minutes.<BR>\n" );
document.write( "How can this be? Please help me to provide an airtight defense or tell me if I should take the plea deal<BR>\n" );
document.write( "instead. I either need to convince the local jurist that she did not speed or convince her that I know she did. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #448356 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=448356\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You cannot take an average of average speeds to get<BR>\n" );
document.write( "a combined average.<BR>\n" );
document.write( "average speed = ( total distance ) / ( total time )<BR>\n" );
document.write( "For the &#64257;rst 5 km she travelled on constant rate of 25 km/hour<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5+=+25%2At+ ALIGN=MIDDLE  ALT=\"+5+=+25%2At+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+1%2F5+ ALIGN=MIDDLE  ALT=\"+t+=+1%2F5+\"   DISABLED_style= \"max-width:90%; height:auto;\" > hr<BR>\n" );
document.write( "Then she traveled at constant rate of 15 km/hour as she climbed the 5 km hill<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5+=+15%2At+ ALIGN=MIDDLE  ALT=\"+5+=+15%2At+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+1%2F3+ ALIGN=MIDDLE  ALT=\"+t+=+1%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > hr<BR>\n" );
document.write( "She rode down the hill at a constant rate of 35 km/hour for the 5 km trip to the city center.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5+=+35%2At+ ALIGN=MIDDLE  ALT=\"+5+=+35%2At+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+1%2F7+ ALIGN=MIDDLE  ALT=\"+t+=+1%2F7+\"   DISABLED_style= \"max-width:90%; height:auto;\" > hr<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "Total distance traveled was <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3%2A5+=+15+ ALIGN=MIDDLE  ALT=\"+3%2A5+=+15+\"   DISABLED_style= \"max-width:90%; height:auto;\" > km<BR>\n" );
document.write( "Total time for trip was <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F5+%2B+1%2F3+%2B+1%2F7+ ALIGN=MIDDLE  ALT=\"+1%2F5+%2B+1%2F3+%2B+1%2F7+\"   DISABLED_style= \"max-width:90%; height:auto;\" > hrs<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+21%2F105+%2B+35%2F105+%2B+15%2F105+=+71%2F105+ ALIGN=MIDDLE  ALT=\"+21%2F105+%2B+35%2F105+%2B+15%2F105+=+71%2F105+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The total time for the trip was <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+71%2F105+=+.676+ ALIGN=MIDDLE  ALT=\"+71%2F105+=+.676+\"   DISABLED_style= \"max-width:90%; height:auto;\" > hrs<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+.676%2A60+=+40.57+ ALIGN=MIDDLE  ALT=\"+.676%2A60+=+40.57+\"   DISABLED_style= \"max-width:90%; height:auto;\" > min<BR>\n" );
document.write( "The is more than the 40 min for the tram, so she wasn't speeding\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );