This morning, while listening to the radio, the DJ was discussing a math problem that appeared on a quiz given by
Mensa, which is an organization of people with very high IQs. The DJ, who admits he only has a high school education, was very proud of himself that he got the problem right. The problem, paraphrased, is:
A cross-country skiier goes 4 miles uphill at 2 miles per hour, and then 4 miles back down at 8 miles per hour. How long did this entire trip take?
When the DJs sidekick gave the answer of 2.5 hours, the DJ then had to look up the answer, and found out that the sidekick, not the DJ, was correct. Then the DJ proceded to explain his incorrect solution: the average speed is 4 miles per hour (
wrong), and so that takes one hour (
wrong again). Even if the speed was 4 miles per hour, that’s two hours for a round trip. Then a caller called up and informed the DJ that the average speed was not 4 miles per hour, he did the math wrong, the average speed is really 5 miles per hour — two mph plus eight mph divided by two — which is also
wrong in this case, but according to the caller, if you use 5 mph, you get the right answer (
wrong again). The DJ apparently had no clue as to why his sidekick got the right answer, even after she explained it, he couldn’t follow the solution. Nor could he see the errors in his own logic, other than the average was 5 mph (which as I said was
wrong).
First, the fact that this is on the Mensa quiz implies that this problem is too hard for ordinary high school graduates. That is a very sad state of affairs, as seventh graders should know how to do this problem. This isn’t a hard problem. But secondly, it seems that a lot of people have learned that an average is a very useful thing, but they haven’t learned when or where to use it properly. And furthermore, the same students have not learned that logic can also be a very useful tool on these problems, even more useful than averaging for many problems.
We live in a technological society. Our society is much better off when people understand how to solve problems like this. Go hug a math teacher today.