Yesterday we gave a school-wide test to many of our high school students. It was part of a monthly, statewide voluntary "fun" competition called the Florida Math League. There are always six questions and they range from pretty simple to pretty tough. Perfect scores are rare. My calculus students usually average about 3 correct, although there is no calculus on the test.
One question caught my eye. Many, many of our bright students got it wrong, but it's a common type of word problem. What do you think? Would you get this one right?
In a 10-km race, First Runner beat second runner by 2 km, and First Runner beat Third Runner by 4 km. If all 3 runners always ran at constant rates, by how many km did Second Runner beat Third Runner.
The answer will be posted below in the comments. If you're a math teacher teaching Algebra II or above, ask your own students and let me know how well they do.
Why do you think so many people get this kind of problem wrong?