A youth group with 26 members is going to the beach. There will also be 5 chaperones that will each drive a van or a car. Each van seats 7 persons, including the driver. Each car seats 5 persons, including the driver. How many vans and cars will be needed?"One, is the problem realistic? Would a real person need to solve this problem?
"Two, is the solution realistic? Would a real person solve the problem using a system of two equations?
"Three, in what ways does this problem help our students become better problem solvers?"
I think he's right, in many ways. The problem he's discussing is contrived and convoluted at best. It does have that "algebra-book word problem from hell" feel about it, but word problems in math textbooks are a funny thing. They have to straddle the line between being realistic and being useful in a classroom for teaching. When constructing a word problem or using one, you need to keep this line in mind. If the word problem doesn't fit your topic, you should change it.
I take a slight issue with the questions, though, in that I don't want to always be asking for a real-world solution that a real-world person would find for a real-world problem.
First, define a "real person". Do I pick me or a mathphobe? If you purposefully want a problem that takes creativity to solve, then separate it from the track you're in. Call it the Puzzle of the Week.
This particular problem doesn't have enough information to come to a single solution anyway - how about adding in the cost per mile of van and car, as well as an additional payment for driver responsibility. Are we trying to minimize cost or make sure all chaperones drive? Do we have a reason to not use the vans unless necessary?