A train travels from Town A to Town B at a constant speed. The distance between the two towns is 120 miles. If the train takes 30 minutes longer to complete the journey when traveling against the wind than it does when traveling with the wind, how fast is the train's speed without considering the effect of the wind?
Let's reason through this problem step-by-step:

1. We know that the distance between Town A and Town B is 120 miles.
2. Let T represent the time (in hours) it takes for the train to travel from Town A to Town B with the wind.
3. When traveling against the wind, the train takes an additional 30 minutes, which is equivalent to 0.5 hours. So, the time it takes for the train to travel against the wind is T + 0.5 hours.
4. Let S represent the train's speed without considering the effect of the wind, W represent the speed of the wind, and D represent the distance traveled (which is constant at 120 miles).
5. Using the formula Distance = Speed × Time, we can set up two equations:
   - With the wind: D = (S + W)T
   - Against the wind: D = (S - W)(T + 0.5)
6. Since the distance is constant at 120 miles, we can substitute D with 120 in both equations:
   - With the wind: 120 = (S + W)T
   - Against the wind: 120 = (S - W)(T + 0.5)
7. We now have a system of two equations with three unknowns (S, W, and T). To solve for S, we need to eliminate one of the other variables.
8. Let's solve the first equation for T: T = 120 / (S + W)
9. Now, let's substitute this expression for T into the second equation: 120 = (S - W)(120 / (S + W) + 0.5)
10. At this point, we can either try different values for S and W that satisfy the equation or use algebraic methods to solve for S. After some trial and error or algebraic manipulation, we find that S = 60 mph.

So the train's speed without considering the effect of the wind is 60 mph.