document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=937207>Question 937207</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Last weekend Oscar traveled by train to visit his grandparents. On Friday he boarded an express train that traveled at an average rate of 85 miles per hour. On Sunday he returned home on a slower train that traveled at an average rate of 51 miles per hour. The total time Oscar spent on the trains last weekend was 8 hours. How many hours did Oscar spend on the train on Friday </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #570642 by </B><A HREF=/tutors/aboutme.mpl?userid=srinivas.g><B>srinivas.g(540)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=srinivas.g><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=srinivas.g><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=570642\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let be x be the time spend on the train on Friday<BR>\n" );
document.write( "ley y be the time  spend on the train on sunday<BR>\n" );
document.write( " total time spend on the trains  = 8 hours<BR>\n" );
document.write( "   x+y =8 ..................eq(1)<BR>\n" );
document.write( "let d be the distance from home to place of grand parents<BR>\n" );
document.write( "   during forward journey ,distance traveled =  speed *time<BR>\n" );
document.write( "                                              =85*x<BR>\n" );
document.write( "during return  journey ,distance traveled =  speed *time<BR>\n" );
document.write( "                                              =51*y<BR>\n" );
document.write( "but in both journeys , distance traveled must be same<BR>\n" );
document.write( "  hence<BR>\n" );
document.write( "              85x =51y<BR>\n" );
document.write( "            move 51y to the left<BR>\n" );
document.write( "  85x-51y =0...................eq(2)<BR>\n" );
document.write( "we need to eq(1), eq(2) to get x, y values<BR>\n" );
document.write( "<TABLE  BORDER=1>\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++++1%5Cx+%2B+1%5Cy+=+8%2C%0D%0A++++85%5Cx+%2B+-51%5Cy+=+0+%29%0D%0A++ ALIGN=MIDDLE  ALT=\"+system%28+%0D%0A++++1%5Cx+%2B+1%5Cy+=+8%2C%0D%0A++++85%5Cx+%2B+-51%5Cy+=+0+%29%0D%0A++\"   DISABLED_style= \"max-width:90%; height:auto;\" >We'll use substitution. After moving 1*y to the right, we get:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Ax+=+8+-+1%2Ay ALIGN=MIDDLE  ALT=\"1%2Ax+=+8+-+1%2Ay\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+8%2F1+-+1%2Ay%2F1 ALIGN=MIDDLE  ALT=\"x+=+8%2F1+-+1%2Ay%2F1\"   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=85%2A%288%2F1+-+1%2Ay%2F1%29+%2B+-51%5Cy+=+0 ALIGN=MIDDLE  ALT=\"85%2A%288%2F1+-+1%2Ay%2F1%29+%2B+-51%5Cy+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and simplify: So, we know that y=5. Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+8%2F1+-+1%2Ay%2F1 ALIGN=MIDDLE  ALT=\"x+=+8%2F1+-+1%2Ay%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, x=3.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Answer: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28+x=3%2C+y=5+%29 ALIGN=MIDDLE  ALT=\"system%28+x=3%2C+y=5+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  </TD></TR>\n" );
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document.write( "                      hence time spend on the train on Friday  = 3 hrs </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );