First, we identify the motion as 1dimensional. We can analyze it using a single axis (x  axis). Let's take the positive direction to be towards the right (towards the east).
The velocity of each train's steam track is equal to velocity of the train + the velocity of the wind.
The train moving west to east (Train 1) has a velocity v, where v >= 0.
The train moving east to west (Train 2) has a velocity v.
The velocity of the wind is w, where w >= 0. It is positive, since it blows from west to east.
The velocity of steam track 1 is equal to the sum of the velocity of Train 1 and the wind velocity, or
V1 = v + w
V2 = v + w.
Speed is the absolute value of velocity, so
S1 = v + w and S2 = v + w. From properties of absolute values, S2 >= S1.
From the problem statement, and what we've just seen about absolute values, we know that we must choose
S1 = 2*S2. Also, since v and w are positive, v+w = v+w. This gives us
v + w = 2v + w. There are two possibilities: Either (v + w) is positive, in which case v + w = v + w, and
v + w = 2(v + w). solving for v,
v + w = 2v + 2w
3v = w, or v = w/3 (1/3 times that of the wind). This is not a choice.
Or (v+w) is negative, in which case v + w = v  w, and
v + w = 2(v  w). Solving for v,
v + w = 2v  2w.
v = 3w (3 times that of the wind). This is answer 1 from your list.
6/22/2015

Gregg O.