Question 1208986
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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>
I prefer a different solution method for a problem like this, like the following.<br>
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>
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>
Let x = # yards the tight end runs after catching the pass
Then x+5 = # of yards the defensive back runs<br>
Since the times are the same, the ratio of numbers of yards is the same as the ratio of their speeds:<br>
{{{x/(x+5)=5/6}}}
{{{6x=5(x+5)}}}
{{{6x=5x+25}}}
{{{x=25}}}<br>
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>
ANSWER: at the tight end's own 45-yard line<br>