document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=42574>Question 42574</A>: <I><SPAN STYLE=\"word-break: break-all;\"> At the beginning of a bicycle race for charity, Roberto and Juana are 30 mi. apart. If they leave at the same time and ride in the same direction, Roberto overtakes Juana in 6 hr. If they ride toward each other, they meet in 1 hr. What are their speeds </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #27689 by </B><A HREF=/tutors/aboutme.mpl?userid=fractalier><B>fractalier(6550)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=fractalier><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=fractalier><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=27689\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let r and j be their respective speeds.<BR>\n" );
document.write( "Well if they ride toward each other and met in 1 hour, they must have a combined speed of 30 mph, since they were 30 miles apart...thus<BR>\n" );
document.write( "r + j = 30<BR>\n" );
document.write( "Now, Roberto overtakes Juana in 6 hours, meaning he must be going 5 mph faster to make up the 30 miles in 6 hours...thus<BR>\n" );
document.write( "r = j + 5<BR>\n" );
document.write( "Substituting this r into the first equation, we get<BR>\n" );
document.write( "j+5 + j = 30<BR>\n" );
document.write( "2j + 5 = 30<BR>\n" );
document.write( "2j = 25<BR>\n" );
document.write( "j = 12.5<BR>\n" );
document.write( "and then<BR>\n" );
document.write( "r = 17.5 </SPAN>\n" );
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