document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=286464>Question 286464</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Juan left home on his bicycle at 10:00 a.m. traveling at 21 km/h. At noon, his brother set out after him on his motorcycle following the same route. If the motorcycle traveled at 63 km/h, what time did Juan's brother overtake him?\r<BR>\n" );
document.write( "\n" );
document.write( "Thank you, sir </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #207796 by </B><A HREF=/tutors/aboutme.mpl?userid=PRMath><B>PRMath(133)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=PRMath><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=207796\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Juan left home on his bicycle at 10:00 a.m. traveling at 21 km/h. At noon, his brother set out after him on his motorcycle following the same route. If the motorcycle traveled at 63 km/h, what time did Juan's brother overtake him? <BR>\n" );
document.write( "Thank you, sir\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "You just need to think of the importance of this equation:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=RT+=+D ALIGN=MIDDLE  ALT=\"RT+=+D\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "In other words, RATE times TIME equals DISTANCE.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now....with that info, make a little chart for yourself:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "________RATE_______TIME______DISTANCE_________\r<BR>\n" );
document.write( "\n" );
document.write( "Juan..............21.........................T............................D............\r<BR>\n" );
document.write( "\n" );
document.write( "Brother........63.........................T -2......................D............\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "See, the brother started out two hours behind Juan, or T - 2.  \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Also, when the brother overtakes Juan, then that means they will be at the exact same place, or the exact distance from the starting point.  In other words: The distance for Juan equals the distance for the Brother.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Knowing that they have to be at the same distance means that you set up an<BR>\n" );
document.write( "equation of:  Distance = Distance (Or D = D)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "SO... let's say: \r<BR>\n" );
document.write( "\n" );
document.write( "D = D    What does \"D\" equal? \r<BR>\n" );
document.write( "\n" );
document.write( " <BR>\n" );
document.write( "\"D\" equals RATE times TIME.  <BR>\n" );
document.write( "For Juan, the RATE times TIME is:  21(T).   <BR>\n" );
document.write( "For the brother the RATE times TIME is 63(T - 2)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Let's fill in that info:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "D = D<BR>\n" );
document.write( "21(T) = 63(T - 2)   Now let's distribute the 63 to the T and 63 to the -2.<BR>\n" );
document.write( "21T = 63T - 126  Now let's subtract 63T from both sides to get the T variables on one side.<BR>\n" );
document.write( "21T - 63T = -126  Now let's subtract:  21T - 63T which is:  -42T<BR>\n" );
document.write( "-42T = -126 Now divide both sides by -42 to further isolate the T.<BR>\n" );
document.write( "T = 3\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now if T equals 3 hours, let's see how that works:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Juan is traveling 21 kmp.  In three hours that's: <BR>\n" );
document.write( "21(T) which is <BR>\n" );
document.write( "21(3) = 63 Kilometers.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The brother is traveling 63 kmp.  In T - 2 hours that's:  <BR>\n" );
document.write( "T - 2 which is 3 -2 = 1<BR>\n" );
document.write( "63(1) = 63 Kilometers.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "SOoo in 1 hour, the brother will be at the 63 kilometer mark. Since the brother took off at noon, in 1 hour it will be 1 pm.  It will also be  1 pm for Juan if he travels for 3 hours from 10 a.m. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I hope this helps you.  And a \"sir\" did not answer your question. :-)  A girl did. :-) Sometimes math types are girls, too. \r<BR>\n" );
document.write( "\n" );
document.write( "Good luck with your math. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );