# 135: Substitute

Substitute |

Title text: YOU THINK THIS IS FUNNY? |

## Explanation

If anything, this comic references the 1993 movie Jurassic Park, like in 87: Velociraptors. The movie deals with a mad billionaire opening an animal zoo. Not so bad, but the animals in question are not your ordinary lions or elephants, but dinosaurs and the like, brought back to life by said billionaire through his DNA-cloning company. Of course, everything goes haywire, and several of the meat-eating creatures, among which the velociraptors mentioned in the image, try to devour every human in the theme park. Said velociraptors possess a certain intelligence for hunting out their prey.

Cueball is asked to substitute for Miss Lenhart in math class. The test he devises contains three questions, which have the recurring theme of humans running from said velociraptors. As Randall himself says in the comic: “This material is more vital than anything you've ever learned,” the joke being that Randall is somehow fearful that such a thing could happen.

Velociraptors, and in particular, the irrational fear of being attacked by them in the modern world, appear several times in xkcd.

Answers to the first two questions can be found in this topic on the forum board, by the way.

## Transcript

- [In a class room, the board says "Math" on the top-left corner, and "Mr. Munroe" in the middle. A stick figure is standing in front of it, speaking to the class.]
- Teacher: Miss Lenhart couldn't be here today, so she asked me to substitute.
- Teacher: I've put out your tests. Please get started.

- [A student in the first row raises the exam paper and says.]
- Student: Mr. Munroe, Miss Lenhart never taught us this.

- Teacher: That's because Miss Lenhart doesn't understand how important certain kinds of math are.
- Student: But this just looks --
- Teacher: This material is more vital than anything you've ever learned
- Student: But --
- Teacher: No buts.

- Teacher: This is a matter of life and death.

- [Excerpt from the exam paper.]
- Name: _________

- [A stick figure is standing, hands over head. A velociraptor is running towards it.]

- 1. The velociraptor spots you 40 meters away and attacks, accelerating at 4 m/s^2 to its top speed of 25 m/s. When it spots you, you begin to flee, quickly reaching your top speed of 6 m/s. How far can you get before you're caught and devoured?

- 2. You're at the center of a 20m equilateral triangle with a raptor at each corner. The top raptor has a wounded leg and is limited to a top speed of 10 m/s.

- [A stick figure is shown in the above situation. The picture has a legend "(Not to scale)".]

- The raptors will run toward you. At what angle should you run to maximize the time you stay alive?

- 3. Raptors can open doors, but they are slowed by them. Using the floor plan on the next page, plot a route through the building, assuming raptors take 5 minutes to open the first door and halve the time for each subsequent door. Remember, raptors run at 10 m/s and they do not know fear.

**add a comment!**⋅

**refresh comments!**

# Discussion

Rikthoff (talk) The issue date is off, as i can't find a create date for the image. Can anyone fix?

1. It takes the raptor 25m/s / 4m/s^2 = 6.25s to reach it's top speed, during which I can run 6.25s * 6m/s = 37.5m. Add on my 40m head start, and I can reach a spot 77.5m away from the raptor before he gets me. In the same time, the raptor can run 4m/s^2 * (6.25s)^2 / 2 = 78.125m. I'm eaten before he's fully up to speed. Therefore, I have to solve for when the raptors location, r(t) = 4m/s^2 * t^2 /2 - 40, and my location, m(t) = 6m/s*t, are equal. Dropping units, we get 2t^2 -40 = 6t, or 2t^2 - 6t - 40 = 0. Dividing by 2 I get t^2 - 3t - 20=0. Using the quadratic equation, I get (3 +/- sqrt(89))/2, roughly equal to 6.217s and -3.217s. Plugging that back into m(t), I get 37.302m for my terminal run. Blaisepascal (talk) 22:18, 14 September 2012 (UTC)

I don't think there is enough information to solve the second problem, because you don't know how fast the non-injured raptors go. Unless you take that information from the first problem. But then, how fast does the wounded raptor accelerate? You would have to find the angle where the wounded and the closest non-wounded raptor would meet you at the same time. 213.127.132.140 17:17, 5 September 2013 (UTC)

With all three raptors and you running at top speeds, I don't think you get caught by the injured raptor and uninjured raptor at the same time. I believe that you must run directly towards the wounded raptor and the two non-injuried raptors will reach you simultaneously before you and the injured raptor meet, and you cannot do better. After all, you can try to run directly away from an uninjured raptor, but you will lose ground to it at a rate of 25-6=19 m/s (but, it is worst for the other uninjured raptor). By running directly at the injured raptor, you lose ground from it at the rate of 10+6=16 m/s. However, if you can accelerate at a rate far above the raptors, I think you could change directions so fast that one raptor could not catch you. However, I am not sure you can keep away from all three indefinitely. --DrMath 04:01, 24 October 2013 (UTC)

For 1 and 2 the solution depends on whether the raptors can accelerate at 2m/s, or they actually increase their speed at this rate. If they just accelerate, It should be possible to do tight circles, and even wind yourself slowly towards another location. I believe this is possible even treating yourself and the raptors as point masses. 2.102.215.18 13:19, 17 July 2013 (UTC)

This could also be a parody of Snape substituting for Lupin (Harry Potter and the Prisoner of Azkaban) in the Defense against Dark Arts class. Snape assigns homework on werewolves, in the hopes of one of the students connecting the dots. Here, Randall might be trying to get the students to suspect that Mrs.Lenhart might be a raptor (out of sympathy, or just being a classhole?). Also 155. 208.124.118.63 18:58, 1 October 2013 (UTC)BK201

There is a problem with the test, as Mr. Munroe wrote it: Question #1 says that a raptor has a top speed of 25 m/s, but question #3 says "Remember, raptors run at 10 m/s...". Furthermore, question #2 says an injured raptor runs at 10 m/s.

- The way I resolved that was that raptors wouldn't be able to run straight long enough to reach their top speed inside of a building. 108.162.237.161 23:53, 27 April 2015 (UTC)

BTW, the answer to question #2 is: run straight toward the injured raptor. The uninjured raptors will run toward you and the injured raptor. Just as you get close to the injured one, slide under his legs. Because he is injured, the uninjured raptors will feast on him instead of you. 173.245.55.227 20:58, 13 December 2013 (UTC)

- This presumes the raptors are cannibalistic. -Pennpenn 162.158.2.221 05:30, 15 June 2015 (UTC)

- I solved it by being a t-rex and just eating the raptors. It's amazing how many math problems become easier when you're a t-rex. 162.158.255.69 23:29, 16 September 2015 (UTC)