document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=637342>Question 637342</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The traveling time is 25 minutes shorter if you higher the average speed by 5 <BR>\n" );
document.write( "km/hour. Raising the average speed by another 5 km/hour lowers the traveling <BR>\n" );
document.write( "time by another 20 minutes. What is the distance of the trail? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #401603 by </B><A HREF=/tutors/aboutme.mpl?userid=Stitch><B>Stitch(470)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Stitch><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=401603\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let trail length = Y<BR>\n" );
document.write( "Let average speed = X<BR>\n" );
document.write( "Let traveling time = T\r<BR>\n" );
document.write( "\n" );
document.write( "We have three unknowns so you need three equations:<BR>\n" );
document.write( "Equation 1: T = Y/X<BR>\n" );
document.write( "Equation 2: T - 25 = Y /(X+5)<BR>\n" );
document.write( "Equation 3: T - 25 - 20 = Y / (X + 5 + 5)<BR>\n" );
document.write( "Rewrite equation 3<BR>\n" );
document.write( "T - 45 = Y / (X + 10)<BR>\n" );
document.write( "----------------------------<BR>\n" );
document.write( "Solve equation 1 for Y<BR>\n" );
document.write( "Equation 1: T = Y/X<BR>\n" );
document.write( "Multiply both sides by X<BR>\n" );
document.write( "T*X = Y<BR>\n" );
document.write( "Substitute T*X into equation 3 for Y<BR>\n" );
document.write( "T - 45 = Y / (X + 10)<BR>\n" );
document.write( "T - 45 = T*X / (X + 10)<BR>\n" );
document.write( "Multiply both sides by (X + 10)\r<BR>\n" );
document.write( "\n" );
document.write( "(X + 10)* (T - 45) = T*X<BR>\n" );
document.write( "Simplify<BR>\n" );
document.write( "T*X - 45X + 10T - 450 = T*X<BR>\n" );
document.write( "Subtract T*X from both sides.<BR>\n" );
document.write( "-45X + 10T - 450 = 0<BR>\n" );
document.write( "Add 45X & 450 to both sides<BR>\n" );
document.write( "10T = 45X + 450<BR>\n" );
document.write( "Divide both sides by 10<BR>\n" );
document.write( "T = 4.5X + 45<BR>\n" );
document.write( "----------------------------<BR>\n" );
document.write( "Now Plug T*X into equation 2 for Y, and use (4.5X + 45) for T<BR>\n" );
document.write( "Equation 2: T - 25 = Y /(X+5)<BR>\n" );
document.write( "T - 25 = T*X / (X+5)<BR>\n" );
document.write( "4.5X + 45 - 25 = ((4.5X + 45)*X) / (X + 5)<BR>\n" );
document.write( "Simplify<BR>\n" );
document.write( "4.5X + 20 = (4.5X^2 + 45X) / (X+5)<BR>\n" );
document.write( "Multiply both sides by (X+5)<BR>\n" );
document.write( "(X+5) * (4.5X + 20) = 4.5X^2 + 45X<BR>\n" );
document.write( "Simplify<BR>\n" );
document.write( "4.5X^2 + 20X + 22.5X + 100 = 4.5X^2 + 45X<BR>\n" );
document.write( "Subtract 4.5X^2 from both sides<BR>\n" );
document.write( "20X + 22.5X + 100 = 45X<BR>\n" );
document.write( "Combine like terms<BR>\n" );
document.write( "42.5X + 100 = 45X<BR>\n" );
document.write( "Subtract 42.5X from both sides<BR>\n" );
document.write( "100 = 2.5X<BR>\n" );
document.write( "Divide both sides by 2.5<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2840+=+X%29 ALIGN=MIDDLE  ALT=\"highlight%2840+=+X%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------------------------------<BR>\n" );
document.write( "Earlier we stated that T = 4.5X + 45.<BR>\n" );
document.write( "Plug 40 in for X and solve for T<BR>\n" );
document.write( "T = 4.5*(40) + 45<BR>\n" );
document.write( "T = 180 + 45<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28T+=+225%29 ALIGN=MIDDLE  ALT=\"highlight%28T+=+225%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------------------------------<BR>\n" );
document.write( "Now plug 40 into equation 1 for X and use 225 for T.<BR>\n" );
document.write( "Equation 1: T = Y/X<BR>\n" );
document.write( "225 = Y/40<BR>\n" );
document.write( "Multiply both sides by 40<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%289000+=+Y%29 ALIGN=MIDDLE  ALT=\"highlight%289000+=+Y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The trail is 9000km<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );