Gifted Issues Discussion homepage Forums General Discussion Alternate approach to algebra problem

Sometimes I only see the obvious so am looking to see if any of you math experts have a quicker approach (other than the two obvious to me) to getting the final answer to the following problem once you set up the equation. You can use factoring covered in the final third/quarter of Algebra I or substitute the five answer choices in the equation. Since DS likes to calculate in his head, it is almost safer to just try the five answer choices, starting with the likeliest ones. The issue is that DS has the conceptual understanding to set up the equation from the problem, but tends to do all calculations in his head so may arrive at the wrong answer when he can't use a calculator.

Here's the problem:

In calm weather, an aircraft can fly from one city to another 200 miles north of the first and back in exactly 2 hours. In a steady north wind, the round trip takes 5 minutes longer. The speed of the wind, in miles per hour, is
A. 8
B. 20
C. 32
D. 35
E. 40

Here's a Solution:
If you let the wind speed be w miles per hour, then the time in hours required for the aircraft to make the roundtrip in the wind is:

25/12 = 200/(200 + w) + 200/(200 - w)

You can obviously use factoring concepts covered in Algebra I(multiply both sides by the product of (200 + w) and (200 - w)) to solve for w. It is not that difficult but susceptible to miscalculations when done in your head. Since you can probably guess at the correct range, it almost may be quicker/safer to substitue the likely answer once you set up the equation.

My question is whether there is a less calculation heavy way to solve this problem. I have been making my living with words so my math is somewhat rusty and I only see the most obvious approaches.