Question 1208986
<pre>
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?

Hint: At time t = 0, the defensive back is 5 yards behind the tight end. 

The tight end can run the 100-yard dash in 12 seconds, so his speed = {{{matrix(1,5, 100/12, "=", 25/3, "yards-per-second", "(y/s)")}}}

The defensive back can run the 100-yd dash in 10 seconds, so his speed = {{{matrix(1,4, 100/10, "=", 10, "y/s")}}}

The tight end catches the pass at HIS OWN 20-yard line with the defensive back at the 15-yard line, and so, the 
tight end is 5 yards ahead of the defensive back.

Let the distance that the tight end (SLOWER player) needs to travel to get to the catch-up point, be D

Since the defensive back (FASTER player) is 5 yards BEHIND the tight end, distance defensive back needs to travel to get
to the catch-up POINT/catch up to the tight end, is (D + 5) yards

Since BOTH will get to the catch-up point at the same time, we EQUATE their respective times to get
the following TIME equation: {{{matrix(4,3, D/(25/3), "=", (D + 5)/10, D(3/25), "=", (D + 5)/10, 3D/25, "=", (D + 5)/10, 3D/5, "=", (D + 5)/2)}}}                            
                              2(3D) = 5(D + 5) ----- Cross-multiplying
                                 6D = 5D + 25
                            6D - 5D = 25
Distance tight end needs to travel to get to catch-up point, or D = 25 yards

Location where tight end caught the ball: HIS OWN 20-yard line
Distance tight end travels to get to catch-up point: 25 yards 
<font color = red><font size = 4><b>The defensive back caught up to the tight end</font></font></b> at the (20 + 25)-MARK, which is <font color = red><font size = 4><b>the tight end's OWN 45 YARD-LINE</font></font></b>.</pre>