document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=963453>Question 963453</A>: <I><SPAN STYLE=\"word-break: break-all;\">  A cat runs 3 times as fast as a mouse. If a mouse runs at 2 meters per second and is 12 m from a cat, the mouse will be caught in _____ seconds. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #588586 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=588586\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if the rate of the mouse is 2 meters per second, then the rate of the cat is 6 meters per second since the cat runs 3 times as fast as the mouse.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the cat is 12 meters from the mouse.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the cat starts chasing the mouse.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the cat has to close the distance between the cat and the mouse.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if the distance the mouse runs is x meters, then the distance the cat has to run is x + 12 meters.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the time that both the cat and the mouse run is the same.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the basic formula is R * T = D\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "for the mouse, this formula becomes 2 * T = D\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "for the cat, this formula becomes 6 * T = D + 12\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "solve both of these formulas for T to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "T = D/2 for the mouse.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "T = (D + 12)/6 for the cat.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since both expressions on the right side of the equations are equal to T, the expressions can be set equal to each other to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "D/2 = (D+12)/6\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "solve for D to get D = 6.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that means that the mouse has run 6 meters and the cat has run 18 meters, at which point in time the cat has caught the mouse.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "let's see if that holds true.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the mouse runs at 2 meters per second for a time of T and runs 6 meters.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this means that the mouse has run for 3 seconds because 2 meters per second * 3 seconds is equal to 6 meters.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "in the same time, the cat has run 6 meters per second * 3 seconds equals 18 meters.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Since the mouse was 12 meters away from the cat to start with, the cat has caught up with the mouse in 3 seconds.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );