document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=831689>Question 831689</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two cyclists, 56 miles apart, start riding toward each other at the same time. One cycles 3 times as fast as the other. If they meet 2 hours later, what is the speed (in mi/h) of the faster cyclist? <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #501573 by </B><A HREF=/tutors/aboutme.mpl?userid=hovuquocan1997><B>hovuquocan1997(83)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=hovuquocan1997><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=501573\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the speed of the slow one be x<BR>\n" );
document.write( "Let the speed of the fast one  be y<BR>\n" );
document.write( "Both travel and meet after 2 hours so we have the equation<BR>\n" );
document.write( "2x + 2y = 56<BR>\n" );
document.write( "Then you have the fast one is 3 times faster than the slow one, so you have<BR>\n" );
document.write( "y = 3x =====>>>> 3x - y = 0<BR>\n" );
document.write( "Then you solve the system of equation<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=linear_substitution.solver>SOLVE linear system by SUBSTITUTION</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Solve:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+system%28+%0D%0A++++2%5Cx+%2B+2%5Cy+=+56%2C%0D%0A++++3%5Cx+%2B+-1%5Cy+=+0+%29%0D%0A++ ALIGN=MIDDLE  ALT=\"+system%28+%0D%0A++++2%5Cx+%2B+2%5Cy+=+56%2C%0D%0A++++3%5Cx+%2B+-1%5Cy+=+0+%29%0D%0A++\"   DISABLED_style= \"max-width:90%; height:auto;\" >We'll use substitution. After moving 2*y to the right, we get:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Ax+=+56+-+2%2Ay ALIGN=MIDDLE  ALT=\"2%2Ax+=+56+-+2%2Ay\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+56%2F2+-+2%2Ay%2F2 ALIGN=MIDDLE  ALT=\"x+=+56%2F2+-+2%2Ay%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Substitute that<BR>\n" );
document.write( "  into another equation:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A%2856%2F2+-+2%2Ay%2F2%29+%2B+-1%5Cy+=+0 ALIGN=MIDDLE  ALT=\"3%2A%2856%2F2+-+2%2Ay%2F2%29+%2B+-1%5Cy+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and simplify: So, we know that y=21. Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+56%2F2+-+2%2Ay%2F2 ALIGN=MIDDLE  ALT=\"x+=+56%2F2+-+2%2Ay%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, x=7.<BR>\n" );
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document.write( "  Answer: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28+x=7%2C+y=21+%29 ALIGN=MIDDLE  ALT=\"system%28+x=7%2C+y=21+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "y=21 so the speed of the faster one is 21mi/h<BR>\n" );
document.write( "TA-DAH<BR>\n" );
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