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" );
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document.write( "Hint: At time t = 0, the defensive back is 5 yards behind the tight end. \r<BR>\n" );
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document.write( "Answer: <font color=red>tight end's own 45 yard line</font>\r<BR>\n" );
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document.write( "Explanation:\r<BR>\n" );
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document.write( "TE = tight end<BR>\n" );
document.write( "DB = defensive back\r<BR>\n" );
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document.write( "Let's find the TE's speed<BR>\n" );
document.write( "distance = rate*time<BR>\n" );
document.write( "d = r*t<BR>\n" );
document.write( "r = d/t<BR>\n" );
document.write( "r = (100 yards)/(12 seconds)<BR>\n" );
document.write( "r = (100/12) yards per second<BR>\n" );
document.write( "r = (25/3) yards per second<BR>\n" );
document.write( "r = 8.3333 yards per second approximately\r<BR>\n" );
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document.write( "DB's speed<BR>\n" );
document.write( "r = d/t<BR>\n" );
document.write( "r = (100 yards)/(10 seconds)<BR>\n" );
document.write( "r = (100/10) yards per second<BR>\n" );
document.write( "r = 10 yards per second\r<BR>\n" );
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document.write( "After x number of seconds, the TE travels a distance of (25/3)x yards.<BR>\n" );
document.write( "Meanwhile the DB travels 10x yards.\r<BR>\n" );
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document.write( "The gap between the players is initially 5 yards.<BR>\n" );
document.write( "Whatever distance the TE travels, the DB must travel that distance plus 5 extra yards to catch up.<BR>\n" );
document.write( "For example, if the TE travels 10 yards, then the DB must travel 10+5 = 15 yards to catch up to the TE.\r<BR>\n" );
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document.write( "DB's travel distance = (TE's travel distance) + 5 yards<BR>\n" );
document.write( "10x = (25/3)x+5<BR>\n" );
document.write( "3*10x = 3*( (25/3)x+5 )<BR>\n" );
document.write( "30x = 25x+15<BR>\n" );
document.write( "30x-25x = 15<BR>\n" );
document.write( "5x = 15<BR>\n" );
document.write( "x = 15/5<BR>\n" );
document.write( "x = 3\r<BR>\n" );
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document.write( "The DB catches the TE at exactly the x = 3 second timestamp.<BR>\n" );
document.write( "The DB catches (and perhaps tackles) the TE exactly 3 seconds after the TE caught the ball. \r<BR>\n" );
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document.write( "After 3 seconds elapse, the TE traveled (25/3)*x = (25/3)*3 = 25 yards.<BR>\n" );
document.write( "The TE goes from the 20 yard line to the 20+25 = <font color=red>45 yard line</font>. <BR>\n" );
document.write( "The TE has <u>not</u> crossed the midway marker since 45 < 50.<BR>\n" );
document.write( "Therefore the TE is still on his side of the field.\r<BR>\n" );
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document.write( "Meanwhile the DB runs 10*x = 10*3 = 30 yards<BR>\n" );
document.write( "The DB goes from the 15 yard line to the 15+30 = <font color=red>45 yard line</font><BR>\n" );
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