Question 1187574
rate * time = distance.


for rob, the formula becomes r * 12 = 100 yards.
for matt, the formula becomes r * 9 = 100 yards.


solve for r to get:


for rob, r = 100/12.
for matt, r = 100/9.


rob catches a pass at his own 20 yard line.
matt is at the 15 yard line directly behind rob.


in order to catch rob, matt has to run 5 more yards than rob in the same amount of time.


let the distance that rob has to run equal to x.
let the distance that matt has to run equal to x + 5.
the time is the same for both.


the formula for rob becomes 100/12 * t = x
the formula for matt becomes 100/9 * t = x + 5


subtract the first equation from the second to get:


100/9 * t - 100/12 * t = 5.


multiply both sides of this equation by (9 * 12) to get:


100*12 * t - 100 * 9 * t = 5 * 9 * 12


simplify to get:


1200 * t - 900 * t = 540


combine like terms to get:


300 * t = 540


divide both sides of the equation by 300 to get:


t = 540 / 300 = 1.8


matt will catch up with rob in 1.8 seconds.


rob starts at the 20 yard line and runs at the rate of 100/12 yards per second for 1.8 seconds.


100/12 * 1.8 = rate * time = a distance of 15 yards.
since he starts at the 20 yard line, he winds up at the 35 yard line.


matt starts at the 15 yard line and runs at the rate of 100/9 yards per second for 1.8 seconds.


100/9 * 1.8 = rate * time = a distance of 20 yards.
since he starts at the 15 yard line, he winds up at the 35 yard line.


the 35 yard line is where matt catches up with rob.