Algebra 2 HELP!?

Question

In a football game, the quarterback is 15 yards away from making a first down and is running at 264 yards per minute. After .03 of a minute, a linebacker who is 15 yards on the opposite side of the first down marker begins running directly towards the quarterback at 440 yards per minute. Will the linebacker be able to tackle the quarterback before he gets the first down? Show all work.

Answer 1

The question is essentially asking, who gets to the first down line first, the quarterback or the linebacker?

This question is equivalent to asking who takes a shorter time to run 15 yards. You also have to consider that the linebacker is giving the quarterback a 0.03-minute headstart.

If it takes the quarterback T minutes to run 15 yards, then the formula is 264 * T = 15. This means that T = 0.056818 minutes. If it takes the linebacker S minutes to run 15 yards, then the formula is 440 * S = 15. This means that S = 0.034091 minutes.

If you add 0.03 minutes to the linebacker's time, you'll find that he'll run the 15 yards to the first down line in 0.064091 minutes. Since it takes the linebacker longer to run the 15 yards, the quarterback would reach the first down line before the linebacker does --> the linebacker would NOT tackle the quarterback before he reaches the first down.

Answer 2

First, you must make a triangle to find the diagonal, the hypotenuse (H).

Side A = 15 yards
Side B = 15 yards
H^2 = 2(15)^2
H^2 = 450
H = 21.21... yards

To cover 15 yards at 264 yards/m, the quarterback needs:
264 = 60 seconds
1 = 60/264
15 = 15*60/264 = 3.41 seconds

1 minute = 60 seconds
.03 minute = 1.8 seconds

To cover 21.21 yards at 440 yards/m, the linebacker needs:
440 = 60 seconds
1 = 60/440
21.21 = 21.21*60/440 = 2.89 seconds

After .03 minute = 2.89 + 1.8 = 4.69

So the linebacker won't be able to tackle the quarterback before he gets the first down.

Answer 3

After .01 minute the quarterback will have traveled 264 *.01 = 2.64 yards leaving an additional 15-2.64 = 12.36 yards to gain the 1st down.

So it will take him 12.36/264 = .046818 minutes to get the 1st down.

Now the linebacker needs to travel 15+ yards to stop the quarterback. So linebacker will run 15 yards in15/440 = .03409 minutes. This means the linebacker will reach the 1st down line .012728 minutes prior to the quarterback. This is over 3/4 seconds so he should make the tackle and preven the 1st down.