Since the problem doesn't tell us anything about the rates and the distance between the two train, there is not much we can say. Statement one tells us that there is 180 miles between the two trains. This is not sufficient, since we don't know how fast the trains are.

Statement 2 alone tells us the rates of the trains, but we don't know how far away they are, this statement alone doesn't help us answer the question.

If we take both statements together however, we can see that the distance that each train would have made when both trains meet, is a total of 180 miles, since both trains were 180 miles away.

We can create the following equation , where  is the time it takes for both train to meet at a given point and  and  are the trains A and B respective rates. The information we have allows us to solve the equation for  and therefore we can answer the problem.

Firstly, we should remember that the average rate is given by the following formula , where  is the total distance and  is the total time. So to answer this question we should find a value for .  can only be found by adding the two times for both trips. By pluging in the values we can find a value for , therefore we need  both statements.

To solve this problem, we need to find the rate of the train considering the fact that the rails are damaged. The first statement tells us only the usual rate of the train and is therefore not sufficient because we don't know how fast the train will be going on the damaged portions of the railroad. 

Statement two only tells us that the train must progress at a rate half as slow as its usual rate. 

Using statements 1 and 2 we can easily find the rate which is given by . Note that this rate is given in miles per minutes but we don't have to calculate it, we just need to know that we can calculate it.

Since we are told an average speed for a round trip we should be able to set the following equation , where  is the distance of a one way and  is the total time of the round trip and  is the average speed of the plane.

Statement 1 tells us that it took the plane twice as long to do the first portion of the round trip, therefore we can figure out  from this statement, indeed,  where  is the time it took to do the second portion of the trip. Therefore, . Since  is the rate for the second portion of the trip, we can figure it out by pluging in the values , which is  sufficient to answer the problem.

Statement 2 tells us that the plane was flying at a speed of , this alone answers the question.

For these types of problems, asking us how long it takes for a vehicle to catch up to another one, we should keep in mind that we can calculate the rate at which the other vehicle is catching up, by doing the difference of the two rates.

From this we can see that we will need both rates for the vehicles as well as the distance between the two vehicles: , where and are the respective rates of vehicles B and A, and  is the distance between the two cars and  is the time it would take for car B to catch up

Statement 1 only tells us the distance between the two vehicle and therefore we don't know how fast car B is catching up and therefore this statement alone is insufficient.

Statement 2 only tells us how fast is the second car going, but here we don't know what is the distance between the two cars.

Therefore, both statements must be taken together to answer this question.

First of all, we should notice that we are looking for a rate and therefore, we should be able to find both a distance and a time for the train to travel that distance.

From statement 1, we can say that  and that  where  is train A's rate and  is the time it takes train B to travel 180 miles. If we manipulate our equations we get : , since 180 are in both equations. But there are two unknowns and neither cancel out. So statement 1 alone is not sufficient.

Statement 2 gives us a rate for train A for an unknown distance, therefore this information is not useful. 

We can see that after using our statements, even together, we still could not find an answer to the problem, therefore statements 1 and 2 together are insufficient.