What I learned working with my older son today

This problem – #15 from the 2006 AMC 10A – is a hard problem:

Problem 15 from the 2006 AMC 10A

“Odell and Kershaw run for 30 minutes on a circular track. Odell runs clockwise at 250 m/min and uses the inner lane with a radius of 50 meters. Kershaw runs counterclockwise at 300 m/min and uses the outer lane with a radius of 60 meters, starting on the same radial line as Odell. How many times after the start do they pass each other?”

I mean **hard**.

My number one struggle in teaching my kids is identifying ahead of time what problems are going to be relatively easy and which ones will be hard. I constantly miss on both sides, and I probably guessed incorrectly on this one by as much as I ever have.

But, spending 20 minutes talking through it helped me get a better feel for why this problem gave him trouble, and also a better feel for the how step by step process you need to go through to solve it. When I read the problem, that step by step process was essentially invisible to me, unfortunately.

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Comments

3 Comments so far. Leave a comment below.
  1. Do you think a square or triangular track shape would have made it easier for him to see the steps?

    • The \pi certainly was one of the steps to climb up on this problem, but only one.

      I showed him how to approximate \pi as 22/7 to make approximate calculations a little easier. That was actually a fun part of the morning and something that I’d not give a lot of thought to previously.

  2. I found this the other day. From Maclaurin’s Treatise on Algebra:

    This is 300 years ago!

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