26) This problem asks us to consider the statements and select the one that is true. We need to go through all the answer choices and eliminate the incorrect ones.
Choices A and B: These choices claim that one train moves faster than the other at all points of the graph. There is an easy way to refute this. We just need to find a point where Train X has a greater speed and a point where Train Y has a greater speed. Since we are given a distance versus time graph, the speed at certain points will be the derivative(the slope) at those points. I'm just going to draw an approximation for the slope.
This diagram clearly shows that at time t = 0, the slope of graph Y is greater. Thus, Train Y has a greater speed at t = 0. However, at time t = T, the slope of graph X is greater; likewise, this means Train X has a greater speed at t = T. We can eliminate choices A and B.
Choices C, D, and E: These choices describe the time it takes for the Trains to move to d[2]. We can simply draw approximately how the graphs would continue.
From this graph, it is noticeable that Train X will reach d[2] before Train Y does. This is described by choice C.
Answer: C
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