A bit ago I got yelled at by a commenter on Kate’s blog who claimed that being always right is why we like math. The problem with that point of view is that, while yes, you can always be right while doing computation, math isn’t just computation. So the other day I was talking with a friend of mine, and that prompted me to post the following tweets:
My friend Phil (@albrecht_letao) responded to the question, and he came up with an answer of $20/hr. When I worked it out with my friend, we came up with $14.25. Does that mean one of us is wrong, since we got different numbers?
No, of course not. What happened is we approached the problems in different ways. Phil only calculated the monetary value: with his amount, my friend would earn the same amount of money she does now. He figured this was an important way to look at it, for paying bills and whatnot. Our calculation came from thinking about how her time is being compensated. Since those 16 hours are being wasted (she has to work them for free; actually, she pays to lose that time), we calculated her “real” hourly rate and used that.
There can be more answers than even these two, depending on what you think is important. But it’s a clear example of a problem, solved using math, with no one right answer. That’s what math is about. I tweeted it thinking maybe it could be a problem worth considering in class, to show that essential idea to students.
What do you think?
P.S. The right answer, of course, came from @calcdave: 
James Cleveland-Tran
The Roots of the Equation 
Comments on: "No Right Answer" (4)
It’s a splendid question. I was surprised the proposed alternate job didn’t come with an estimate of how long the commute there would be, though that maybe would give away that accounting for the time spent commuting is part of the trouble in building the model on which one’s to calculate.
Oh, she mentioned it to me, though I didn’t tweet it. (It’s 30 min a day, so 2.5 hrs a week.) I suppose if I were to present the problem to students I would withhold that info unless asked for it.
It only seems right to me that if you’re going to account for travel time with one job, you should with the other as well
True, though there is also a difference in travel: one is the terrible LIRR plus walking, and the other is a short drive. So how do you quantify that difference?