Sunday, January 04, 2009

Stevens Pass Day 6: Twilight, Math, Burn

FUN MATH QUESTION AT THE BOTTOM!!!

Oh man, I wish I had brought my camera today. I checked numerous weather forecasts last night and they all said a big storm was coming late today. With my luck, I decided not to get greedy--go early and leave early. I made it up to the mountain just before opening, and the views on the drive there were spectacular. High clouds with a slit of blue sky between the clouds and the mountains, which let the sunrise beam through and light up the mountain in what I can only describe as twilight blue. The clouds ranged from salmon to yellow, it was a very good wake up distraction.

I took Big Chief to Southern Cross, the quickest way to the backside at Stevens, and was greeted with another amazing view. I was now above the clouds, and could see mountain tops all around, with the clouds covering the valleys. The chair lift descended into the abyss on the backside, and I followed it to the bottom, with a smile and burning legs. I rode ten chairs on the backside, all involving double-diamond terrain, and I got worked out. At one point, the lift operator said, "Nice face shots!"

I looked at him quizzically, then he pointed to his face and said, "Your beard--it is covered in snow!"

Cool! I had only fallen once, and that is when one of my skis came off from a rather jarring hit with a mogul--but I stopped on my remaining ski without face-planting. The snow on my beard must have been from a face shot I was unawares of, sneaky face-shots.

As I rode the chair lifts up I came up with a math problem for my future students, involving the number of chairs on the lift, the time it takes to reach the top, and the individual number of each chair. I haven't hammered out all the details yet, but I'm thinking of asking something along the lines of:

1a) Chairs on a chair lift are numbered 1 to 200 consecutively. At the beginning of the lift you are on chair 1. In front of you is chair 200 and directly across from you is chair 2. Just as you get on chair 1, chair 102 unloads at the top of the lift and is directly across from chair 101. After riding the chair for 8 seconds, you are still on chair 1, but now directly across from you is chair 4. How long does it take you to unload at the top of the lift?

1b) Now you are on chair 35, and directly across from you is chair 200. How much longer until you unload?

Guesses? Show your work!

Extra credit question: is this skiing type of question one that would favor well-to-do kids over low-income kids? Is it still worth using in class if it favors one subset of kids over another?

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6 Comments:

Blogger SirFWALGMan said...

Trick questions. Some retard with her 5 rug rats will hold the whole fucking lift up before you get to the top.. or maybe that blind guy.. You can not factor in the retard factor so thus the question can not be answered.

6:03 AM  
Blogger MHG said...

Partial credit...

7:47 AM  
Blogger DrChako said...

I love Waffles.

Okay - at zero seconds you are across from chair 2. At 8 seconds you are across from chair 4. That means you pass a chair going in the opposite direction every 4 seconds. Chair 200 will be across from you when you unload. That means you will pass 198 chairs from when you get on until you unload. If you start counting right when you get on the chair you have 13 minutes 12 seconds (792 seconds) until you get off. If you start counting as you pass chair 4 (which is possible based on the way you asked the question), you have 784 seconds.

Question 1b is easier. There are the same number of chairs in front of you as behind chair 200. 200-35=165 chairs. Since it's an odd number, there is obviously a chair at the apex of the lift turn. that means there are 82 chairs until you get off. 82*4=328 seconds until you get off, since you pass a chair every 4 seconds.

And finally, screw classism. This is math!

-DrC

12:57 PM  
Blogger MHG said...

Dr. Chako,

Your two answers seem to be quite far apart. 792 seconds vs. 328 seconds, with only 35 chairs missing in question two. Why is this?

MHG

1:23 PM  
Blogger Memphis MOJO said...

Let's see, at 0 seconds you are, um, wait at 4 seconds you are across from the, um....let me get back to you, I'm too busy looking at the great scenery.

6:59 AM  
Blogger The Wife said...

Something is off in your chairlift configuration, methinks . . . I tried to do it graphically and couldn't get it to work.

Except I think the Dr. is wrong. We'll map it out tonight.

But I applaud you for your social consciousness in realizing the potential bias in your question (poor kids, kids from Hawaii, kids who live in the desert . . . ).

I applaud Waffles for recognizing the practical ramifications of the question in that some moron eventually can't figure out how to unload properly and screws things up.

1:45 PM  

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