document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1113774>Question 1113774</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A man finds that he can reach a certain town in 6 hours by traveling 240 miles on an interstate highway and then changing to local roads for 80 miles. He can also get there by traveling 270 miles on a different interstate then proceeding 40 miles on a local highway. This route saves 1/2 hour. If he averages x mph on interstates and y on local roads, find his average speed on the interstate and on local roads.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #728857 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</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=728857\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "By the first route, the time on interstates is 240/x and the time on local roads is 80/y; by the second route, the respective times are 270/x and 40/y.<br><BR>\n" );
document.write( "The total time for the first route is 6 hours; for the second it is 5.5 hours.<br><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=240%2Fx%2B80%2Fy+=+6 ALIGN=MIDDLE  ALT=\"240%2Fx%2B80%2Fy+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" >;<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=270%2Fx%2B40%2Fy+=+5.5 ALIGN=MIDDLE  ALT=\"270%2Fx%2B40%2Fy+=+5.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Don't make the mistake of trying to get rid of the variables in the denominators -- the required work will be FAR harder than necessary.  Solving the pair of equations in their current form is easy.<br><BR>\n" );
document.write( "Multiply the second equation by 2 and subtract one equation from the other to eliminate y:<br><BR>\n" );
document.write( "(3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=540%2Fx%2B80%2Fy+=+11 ALIGN=MIDDLE  ALT=\"540%2Fx%2B80%2Fy+=+11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(4) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=300%2Fx+=+5 ALIGN=MIDDLE  ALT=\"300%2Fx+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x+=+300 ALIGN=MIDDLE  ALT=\"5x+=+300\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+60 ALIGN=MIDDLE  ALT=\"x+=+60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Substitute into either original equation to find y:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=240%2F60%2B80%2Fy+=+6 ALIGN=MIDDLE  ALT=\"240%2F60%2B80%2Fy+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2B80%2Fy+=+6 ALIGN=MIDDLE  ALT=\"4%2B80%2Fy+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=80%2Fy+=+2 ALIGN=MIDDLE  ALT=\"80%2Fy+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y+=+80 ALIGN=MIDDLE  ALT=\"2y+=+80\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+40 ALIGN=MIDDLE  ALT=\"y+=+40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Answer: 60mph on interstates; 40mph on local roads.<br><BR>\n" );
document.write( "Check...<BR>\n" );
document.write( "1st route: 240/60+80/40 = 4+2 = 6<BR>\n" );
document.write( "2nd route: 270/60+40/40 = 4.5+1 = 5.5 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );