Seting up the equation is not a problem for DS - he learned d=rt in the 4th grade science unit on motions.
I was trying to use a shorthand - you are correct that it is not actually factoring but once you covered the factoring concepts in Algebra I, you would learn to remove the variable from the denominator by multiplying by (200 + w)(200 - w) to solve for w.
In this particular case, because the numbers in the equation are small and I can sense which numbers are more likely, it actually takes less time to arrive at the correct answer by substitution than by solving for w.
I see your point about long term learning, but this situation actually has nothing to do with that. In a real school situation, he would either need to lay out many of the steps for essay problems or simply use his calculator to check his answer to avoid careless calculation errors for multiple choice questions. This problem is in the context of no calculator plus time contraint.
