On 1 October 2000, Marilyn vos Savant's column contained the following problem sent by Joe Black of Athens, TX. "Say that two motorboats on opposite shores of a river start moving toward each other, but at different speeds. (Neglect all other factors, like acceleration, turn-around and current.) When they pass each other the first time, they are 700 yards from one shoreline. They continue to the opposite shore, then turn around and start moving toward each other again. When they pass the second time, they are 300 yards from the other shoreline. (Their speeds, although different, remain constant.) How wide is the river?"
On 19 November 2000, Marilyn published the following letter from Peter Mantos of Albuquerque, NM. "I found it interesting that the recent motorboat/river problem is _not_ solvable in a straightforward mathematical way: The problem appears to have five unknowns and only four equations. But you demonstrated that it can be solved with pure logic!"
Marilyn says that she has "heard from 462(!) readers, including plenty of mathematicians and other professionals, who fervently believe my answer is wrong."
Although there is overwhelming evidence that many professionals are completely stumped by Algebra I problems, I am surprised that any mathematician would question her answer.
When I first read the problem, I worked on it without reading her solution. I made the same observations 1), 2) and 3) that Marilyn made, but I did not reach her observations 4) and 5). Based on the way I was taught by Miss Phoebe Fitzpatrick, I identified one unknown and tried to derive an equation. The first equation reduced to an identity. The second yielded a quadratic equation with the same solution that Marilyn obtained logically.
The second letter is indicative of the twisted way in which Algebra I continues to be taught. It gives readers the fallacious impression that this "problem is _not_ solvable in a straightforward mathematical way: The problem appears to have five unknowns and only four equations." Why does Marilyn continue to promote this type of nonsense?