Critical thinking skills seem to become more rare as time passes. Allied with that is the notion that people, in a way like airplane pilots, seem operate more and more on autopilot. I once gave a lecture on critical business thinking to a roomful of very senior executives. Challenging them to solve a simple problem, I suggested that (a) at least 90% would get it wrong. I told them to write down their answers and not blurt it out. The problem was as follows:
A car traverses a 1 mile track at a constant 30 miles per hour. At what speed must the car go on a 2nd lap to average 60 mph for the 2 laps.
Easy, right? Well, right away, one of the big cheeses blurted out, "That's simple! The answer is 90!" I asked that everyone turn in their answers. Then, that rather, self-assured individual got quite upset when I told him he was wrong. He said, "Oh, come on, everyone knows the average of 30 and 90 is 60." He got even more upset when I said "Not in this case." The audience was even more taken aback when I told them that only two other people got the right answer. I explained that they hadn't thought about the other (than speed) major variable in the problem - time. To average 60 mph, which is a mile a minute, you have to do the two laps in two minutes. Unfortunately, running the first 1 mile lap at 30 mph used 2 minutes, making it impossible to ever reach the 60 mph average for two laps, regardles of fast you went on the 2nd lap. You could theoretically approach infinite speed on the second lap but never make it since the two minutes had already elapsed on the first lap. Thus, I introduced the idea of critically thinking about the hidden variables in business considerations, one of which is time.
I never got invited back to address that group. The folks who put the meeting together said I embarrassed those executives and they didn't like it. It should be noted that this problem is a good way to first introduce a student to Calculus if not a group of hide-bound executives to critical thinking.
