SOLUTION: Hello there. I need some help with the following word problem please and thank you in advance! Rob Gronowski of the New England Patriots can run 100 yards in 12 seconds, and Ma

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Question 1187574: Hello there. I need some help with the following word problem please and thank you in advance!
Rob Gronowski of the New England Patriots can run 100 yards in 12 seconds, and Matt Forte of the New York Jets can run 100 yards in 9 seconds. Suppose that Gronowski catches a pass at his own 20-yard line in stride and starts running away from Forte, who is at the 15-yard line directly behind Gronowski. At what yard line will Forte catch up to Gronowski?
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
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.





Answer by MathTherapy(10553)   (Show Source): You can put this solution on YOUR website!

Hello there. I need some help with the following word problem please and thank you in advance!
Rob Gronowski of the New England Patriots can run 100 yards in 12 seconds, and Matt Forte of the New York Jets can run 100 yards in 9 seconds. Suppose that Gronowski catches a pass at his own 20-yard line in stride and starts running away from Forte, who is at the 15-yard line directly behind Gronowski. At what yard line will Forte catch up to Gronowski? 
Let distance that Gronowski needs to run, to get to catch-up point, be D
Then Forte will need to cover a distance of D + 5, to get to catch-up point
We then get the following TIME equation: 
                                           4(3D) = 9D + 45 ---- Multiplying by LCD, 100
                                             12D = 9D + 45
                                        12D - 9D = 45
                                              3D = 45
Distance that Gronowski needs to run to get to catch-up point, or 

Gronowski, after catching the ball at the 20 yard-line, will need to run 15 yards to get to the catch-up point.
This will get him to the 20 + 15 = 35-yard line before Forte catches up to him.

OR

Forte will need to run 20 (15 + 5) yards to get to the catch-up point. And, since he was at the 15-yard line
when Gronowski caught the ball, he'll get to the 15 + 20 = 35-yard line in order to catch up to Gronowski.
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