document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1208986>Question 1208986</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A tight end can run the 100-yard dash in 12 seconds. A defensive back can do it in 10 seconds. The tight end catches a pass at his own 20-yard line with the defensive back at the 15-yard line. If no other players are nearby, at what yard line will the defensive back catch up to the tight end?\r<BR>\n" );
document.write( "\n" );
document.write( "Hint: At time t = 0, the defensive back is 5 yards behind the tight end. \r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #847804 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=847804\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The response from the other tutor shows a formal algebraic solution using a variation of what is probably the most common method, and very likely the method taught in most references.<br><BR>\n" );
document.write( "I prefer a different solution method for a problem like this, like the following.<br><BR>\n" );
document.write( "The tight end and the defensive back can run the 100-yard dash is 12 seconds and 10 seconds, respectively.  Since those distances are the same, the ratio of their speeds is 10:12 = 5:6.<br><BR>\n" );
document.write( "When the tight end catches the pass, he is 5 yards past the defensive back.  So he will catch up to the tight end when he has run 5 yards farther than the tight end.<br><BR>\n" );
document.write( "Let x = # yards the tight end runs after catching the pass<BR>\n" );
document.write( "Then x+5 = # of yards the defensive back runs<br><BR>\n" );
document.write( "Since the times are the same, the ratio of numbers of yards is the same as the ratio of their speeds:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F%28x%2B5%29=5%2F6 ALIGN=MIDDLE  ALT=\"x%2F%28x%2B5%29=5%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x=5%28x%2B5%29 ALIGN=MIDDLE  ALT=\"6x=5%28x%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x=5x%2B25 ALIGN=MIDDLE  ALT=\"6x=5x%2B25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=25 ALIGN=MIDDLE  ALT=\"x=25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "From the time the tight end catches the pass until the defensive back catches up to him, the tight end runs x = 25 yards and the defensive back runs x+5 = 30 yards.  Since the tight end catches the pass at his own 20-yard line, the yard line where the defensive back catches him is 20+25 = 45.<br><BR>\n" );
document.write( "ANSWER: at the tight end's own 45-yard line<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );