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