Two missiles are approaching one another moving at 9,000 mph and 21,000 mph, respectively. How far apart are they 1 minute before they collide? 9,000/60 gives 150 miles per minute. 21000/60 gives 350 miles per minute. Put those together and you get 500 miles in two minutes. Because we want to get one minute, divide 500 by 2. The missiles are 250 miles apart before they collide. -A presentation by two students.

The class buys it. I express confusion: Isn’t there just one minute we’re talking about? Exactly! The whole class responds—they’re so pleased I finally get it—That’s why we have to divide by 2!

By the norms of the class, if the community buys the argument, the presenters can submit the paper. It still has to pass review, however, and I’m the reviewer.

The goal, of course, is to avoid the completely useless path of simply telling them the answer is 500 and they’re just wrong. As far as I can tell, it is precisely as obvious to them that the answer is 250 miles as it is to me that the answer is 500 miles. Their answer makes sense to them, and my answer doesn’t. That’s what I need to reverse.

So I offer my burden up to the blogosphere: What question can I ask my two junior colleagues that will help them see what I’m talking about? Or, as a distant second choice: what’s a clear way I can explain to them why it’s 500 miles and not 250?