document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=444681>Question 444681</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In one hour, Steve drives 25 miles farther in his car than John can cycle on his bike. If it takes John an hour and a half hours longer to cycle seventy five miles than it takes Steve in his car, how fast can John cycle? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #306727 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=306727\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In one hour, Steve drives 25 miles farther in his car than John can cycle on his bike.<BR>\n" );
document.write( "If it takes John an hour and a half hours longer to cycle seventy five miles than it takes Steve in his car, how fast can John cycle?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let c = speed that John can cycle<BR>\n" );
document.write( "Let d = speed Steve can drive<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Write a distance equation for the statement:<BR>\n" );
document.write( "\"In one hour, Steve drives 25 miles farther in his car than John can cycle on his bike. \"<BR>\n" );
document.write( "Steve's dist - John's dist = 25<BR>\n" );
document.write( "1d - 1c = 25<BR>\n" );
document.write( "d = (c + 25)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Write a time equation for the statement, (time = dist/speed):<BR>\n" );
document.write( "\"If it takes John an hour and a half hours longer to cycle seventy five miles than it takes Steve in his car,\"<BR>\n" );
document.write( "John's travel time - Steve's travel time = 1.5 hrs<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=75%2Fc ALIGN=MIDDLE  ALT=\"75%2Fc\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=75%2Fd ALIGN=MIDDLE  ALT=\"75%2Fd\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1.5<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Replace s with (c+25)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=75%2Fc ALIGN=MIDDLE  ALT=\"75%2Fc\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=75%2F%28%28c%2B25%29%29 ALIGN=MIDDLE  ALT=\"75%2F%28%28c%2B25%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1.5<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Multiply by c(c+25), results<BR>\n" );
document.write( "75(c+25) - 75c = 1.5c(c+25)<BR>\n" );
document.write( "75c + 1875 - 75c = 1.5c^2 + 37.5c<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Arrange as a quadratic equation<BR>\n" );
document.write( "1.5c^2 + 37.5c - 1875 = 0<BR>\n" );
document.write( ";<BR>\n" );
document.write( "Get rid of those decimals, multiply by 2<BR>\n" );
document.write( "3c^2 + 75c - 3750 = 0<BR>\n" );
document.write( ":<BR>\n" );
document.write( "You can solve this using the quadratic formula, but this will factor to<BR>\n" );
document.write( "(3c + 150)(c - 25) = 0<BR>\n" );
document.write( ":<BR>\n" );
document.write( "The positive solution<BR>\n" );
document.write( "c = 25 mph is the cycling speed<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "To check this; find the driving speed<BR>\n" );
document.write( "d = c+25<BR>\n" );
document.write( "d = 50 mph<BR>\n" );
document.write( "Find the time of each<BR>\n" );
document.write( "75/25 = 3 hrs<BR>\n" );
document.write( "75/50 = 1.5<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "differ: 1.5 hrs\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );