215k views
4 votes
Two defenders and the ball carrier start at the 40-yard line. Defender 1 starts 10 yards away from the ball carrier to the ball carrier’s left. Defender 2 starts 30 yards away from the ball carrier to the ball carrier’s right. Defender 1 runs 1.1 times as fast as the ball carrier. Defender 2 runs 1.25 times as fast as the ball carrier. Will either defender be able to reach the ball carrier before he runs the 40 yards he needs to reach the end zone and score a touchdown? Provide evidence to support your answer.

1 Answer

3 votes

Final answer:

Neither defender will be able to reach the ball carrier before he reaches the end zone and scores a touchdown.

Step-by-step explanation:

To determine whether either defender can reach the ball carrier before he reaches the end zone, we can calculate the time it will take for the ball carrier to run 40 yards and compare it to the time it will take for each defender to reach the ball carrier.

First, let's calculate the speed of the ball carrier. We know that he runs 40 yards in the same amount of time it takes for Defender 1 to run 10 yards and for Defender 2 to run 30 yards, so the ratio of their speeds is 40:10:30.

Since Defender 1 runs 1.1 times as fast as the ball carrier, we can set up the equation 40/x = 10/(1.1x) to find the speed of the ball carrier, where x is the speed of the ball carrier. Solving this equation, we find that x = 10/1.1 = 9.0909 yards per second.

Similarly, since Defender 2 runs 1.25 times as fast as the ball carrier, we can set up the equation 40/x = 30/(1.25x) to find the speed of the ball carrier, where x is the speed of the ball carrier. Solving this equation, we find that x = 30/1.25 = 24 yards per second.

Now, let's calculate the time it will take for each defender to reach the ball carrier. Defender 1 needs to cover a distance of 10 yards, so he will take 10/9.0909 = 1.1 seconds. Defender 2 needs to cover a distance of 30 yards, so he will take 30/24 = 1.25 seconds.

Since both defenders take more time to reach the ball carrier than it takes for the ball carrier to run 40 yards, neither defender will be able to reach the ball carrier before he reaches the end zone and scores a touchdown.

User Sauumum
by
7.4k points