Comments on: A Train Leaves Chicago Traveling At Who Cares?

By: abcde

abcde — Mon, 25 Jul 2011 07:58:10 +0000

Very good question! Clearly I did not think this all the way through. But I just have this classic image of the two people fighting over the ultimate weapon from all the action flicks I’ve watched. Perhaps you can judge a person’s speed by their appearance. How fit do they look?

By: Dan Meyer

Dan Meyer — Mon, 25 Jul 2011 05:20:24 +0000

How does Person A know that Person B runs 12 mph?

By: abcde

abcde — Mon, 25 Jul 2011 05:09:58 +0000

Another “real-life” scenario that mirrors the train problem involves battles to the death. You encounter these most often in cheesy action flicks, but I’m sure in-the-moment calculation skills can come in handy for the everyday citizen.

Imagine that two people are in a warehouse gunfight, trying to kill each other from opposite sides. The camera cuts back and forth, as bullets whizz by and create sparks from the ricocheting. Soon, both warriors are out of ammo.

But the battle isn’t over. The camera zooms in on an object that happens to lie on the warehouse floor. It is a machete. Both fighters see it at the same time. They make eye contact, each acknowledging what is about to happen. Simultaneously, they begin a mad dash to the machete.

The catch, of course, is that the machete is not directly in between them. Maybe it lies 10 feet closer to person A. But person A can only sprint at 8mph, while person B can hit 12mph (I just pulled these speeds out of a hat).

Who’s going to die?

If a person can, at this very moment, perform this mental calculation, perhaps s/he an decide whether it makes sense to run after the machete or simply flee.

By: Weekly Picks « Mathblogging.org — the Blog

Weekly Picks « Mathblogging.org — the Blog — Wed, 20 Jul 2011 09:49:25 +0000

[…] maybe Conrad Wolfram in this interview you can see on Wild About Math! has some ideas for you. Also dy/dan (and commenters) muse about how to make stereotypical problems more appealing, while digitizor has found one nice example how this can be done (via la covacha mathemÃ¡tica). […]

By: Kelly Berg

Kelly Berg — Wed, 13 Jul 2011 14:05:44 +0000

A few years ago there was a TV series called The Eleventh Hour on CBS. In this episode titled Subway, the main characters are trying to find out where and when 5 people may have intersected in the busy subway system. When the episode orginally aired, my pre-calculus kids had just finished a unit on parametric equations. I couldn’t hit record fast enough!! It was an excellent use of transforming a mundane topic into the “testimonial” of math interlinking with the world, albeit Hollywood style. Now, I use this activity to facilitate a great discussion on the when and the where and why it might be important. The students usually are jumping at the chance to now use parametric equations to solve the “Train A leaves…” problem.

By: Dan Meyer

Dan Meyer — Tue, 12 Jul 2011 18:42:25 +0000

@Belinda, I suppose I'd put this problem somewhere in the neighborhood of d = r * t. Its appeal (to me) is as an example of combined rates. Also, as is the case with all application problems, we're implicitly trying to sell students on the power of math to explain the world they live in. Many other commenters have mistaken my efforts here at increasing engagement. My point here, instead, is to improve the testimonial, to craft a better sales pitch for the tight link between math and the world. I'm worried, all of the sudden, that readers of this blog are too convinced of that link already to empathize with those who are not. (ie. students who dislike math and find it pointless.) What efforts do you take to put yourself into your students' heads? When you get in there, do you find yourself impressed by your own efforts? I follow up here.

By: dy/dan » Blog Archive » A Train Leaves Chicago Traveling At Who Cares, Ctd.

Tue, 12 Jul 2011 18:29:55 +0000

[…] of the responses to my last post focused on narratives to hang around the old math problem –Â lovers meeting, trains nearly […]

By: Garth

Garth — Tue, 12 Jul 2011 18:02:43 +0000

Here is an equivalent problem that has a real aspect, since I have actually had to do this many times and, being a math geek even then, have tried to solve the problem while executing it.
A column of soldiers 100 yards long is marching along the road at 5 mph. The 1st Sergeant needs to get from the tail of the column to the head of the column. If he walks at a rate of 7 mph how long will it take him to reach the head of the column? The history of this problem seems to be rather long. I have seen the same basic problem involving a column of Napoleon’s soldiers and a horseman riding around the column. This could also be the “how long does it take car A to catch car B” type of problem. The car A catching car B type problem is regularly applied in racing situations. Right now the Tour de France managers are constantly calculating this type of problem during the race to predict the time required to capture a break-away. The same problem is computed by race directors at car and motorcycle races. These situations may not be as exciting as two trains colliding but they are real world and are regularly being applied and solved. There are a lot of video clips of the Tour commentators discussing the catch-up time.

By: luke hodge

luke hodge — Tue, 12 Jul 2011 17:08:54 +0000

Paul,

The following is somewhat related to your plan:

It is in a bit of a draft stage, but essentially is two different size tires racing. One has a head start and one is travelling faster. The twist is that you can only directly observe rotational speeds of the wheels. It is not so easy to get the speeds, camera angles, and so forth right.

By: Gretchen Eastman

Gretchen Eastman — Tue, 12 Jul 2011 15:56:39 +0000

One could possibly use clips from the movie “Unstoppable.” It has a lot of good what-if’s related to trains either hitting or just missing each other. It’s “Speed” but on train tracks.