document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1195601>Question 1195601</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A tortoise makes a journey in two parts; it can either walk at 4 cm/s or crawl at 3 cm/s. If the tortoise walks the first part and crawls the second, it takes 110 seconds. If it crawls the first part and walks the second, it takes 100 seconds. Find the lengths of the two parts of the journey. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #828153 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=828153\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The response from the other tutor shows a good standard method for solving the problem.<br><BR>\n" );
document.write( "But the numbers in this problem allow for a somewhat different solution method that some students might (or might not!) find easier.<br><BR>\n" );
document.write( "If x and y are the lengths of the first and second parts of the journey respectively, then we have two equations:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F4%2By%2F3=110 ALIGN=MIDDLE  ALT=\"x%2F4%2By%2F3=110\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F3%2By%2F4=100 ALIGN=MIDDLE  ALT=\"x%2F3%2By%2F4=100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Multiply both equations by the least common denominator, 3*4=12:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B4y=1320 ALIGN=MIDDLE  ALT=\"3x%2B4y=1320\"   DISABLED_style= \"max-width:90%; height:auto;\" > [1]<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2B3y=1200 ALIGN=MIDDLE  ALT=\"4x%2B3y=1200\"   DISABLED_style= \"max-width:90%; height:auto;\" > [2]<br><BR>\n" );
document.write( "Now, instead of using the standard algebraic method of solving the pair of equation using elimination, let's add these last two equations and simplify:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x%2B7y=2520 ALIGN=MIDDLE  ALT=\"7x%2B7y=2520\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=2520%2F7 ALIGN=MIDDLE  ALT=\"x%2By=2520%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=360 ALIGN=MIDDLE  ALT=\"x%2By=360\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Now use this equation with equations [1] and [2] to solve the problem.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B3y=1080 ALIGN=MIDDLE  ALT=\"3x%2B3y=1080\"   DISABLED_style= \"max-width:90%; height:auto;\" > [3]<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B4y=1320 ALIGN=MIDDLE  ALT=\"3x%2B4y=1320\"   DISABLED_style= \"max-width:90%; height:auto;\" > [1]<br><BR>\n" );
document.write( "Subtract [3] from [1]:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=240 ALIGN=MIDDLE  ALT=\"y=240\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B3y=1080 ALIGN=MIDDLE  ALT=\"3x%2B3y=1080\"   DISABLED_style= \"max-width:90%; height:auto;\" > [3]<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2B3y=1200 ALIGN=MIDDLE  ALT=\"4x%2B3y=1200\"   DISABLED_style= \"max-width:90%; height:auto;\" > [2]<br><BR>\n" );
document.write( "Subtract [3] from [2]:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=120 ALIGN=MIDDLE  ALT=\"x=120\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Obviously we get the same answers -- by a different path.<br><BR>\n" );
document.write( "ANSWERS: The first part of the journey is x=120cm; the second part is y=240cm.<br><BR>\n" );
document.write( "CHECK:<BR>\n" );
document.write( "x/4+y/3 = 120/4+240/3 = 30+80 = 110<BR>\n" );
document.write( "x/3+y/4 = 120/3+240/4 = 40+60 = 100<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );