Flipping the Mathematical Bird

I believe that when it comes to problem solving, the following can be said:

• There are many incorrect ways to solve a problem, even if the outcome is correct
• There are very few correct ways to solve a problem, often only one

That being said, I pose the following 5th grade math "word problem." The important thing to note about this particular problem is that there are at least two obvious ways to figure out the solution. One is the right method, the other, although technically correct, isn't nearly as eloquent. I'll make the numbers easy, and if no one figures out the right method to solve the problem, I'll make it known in a future post. Here we go...

Two trains are heading straight toward each other on the same set of tracks. They are currently 100 miles apart and each is traveling at 5 miles per hour. There is a bird that continually flies back and forth between the trains as they approach each other. The bird flies at 20 miles per hour. How far will the bird have flown when the trains meet each other?

Notes:

• Don't worry about the physical/logistical details... you're missing the point
• Don't cheat by reading other people's posts (at least not until after you have come up with your solution)... you're missing the point
  
• Don't Google it... you're missing the point
• If this takes you more than a few minutes, you're not using the right method to solve the problem
• If you start writing down lots of calculations on a piece of paper, you're not using the right method to solve the problem
• This can easily be calculated in your head
• Mathematically inclined people tend to choose the wrong method to get the solutions

The moral of this is that being smart, intelligent, or some kind of a genius in a given area doesn't necessarily mean that you know the best way of solving a problem. Often, simply a different view of a problem, even if naive, can still yield the right methodology. The real problem is getting smart, intelligent, and/or genius-types to accept that their method is not the best.