A train takes two hours to travel from one station to the other.

Responding to a pm:

Here is the thing about average speed - it is not constant speed.
If my average speed is 50 mph for an hour, all I can say is that I took 1 hour to cover 50 miles of distance. At what speed I actually drove, I cannot say. For some mins, I could have driven at 20 mph, for some I could have driven at 80 mph and so on. Overall, whatever I did, it led to me covering 50 miles in 1 hour.

(1) The train covers one-third of the total distance in the first hour at an average speed of 80 mph.
The average speed of the train was 80 mph. This means the train covered 80 miles in the first hour - that is all the information I get. At what speed did the train actually run at different times, we cannot say.
We are also given that it covers 1/3rd of the distance in this one hour. So 80 miles is 1/3rd of the total distance.
Hence total distance must be 240 miles. This is what we were asked.
Hence, sufficient.

(2) The average speed during the second hour is 160 mph.
This tells us that the train covered 160 miles in the second hour. But without using data from stmnt 1, we cannot say how much distance it covered in the first hour. Hence this statement alone is not sufficient.

Answer (A)