Final answer:
The rate of the eastbound train can be calculated by setting up an equation based on the fact that it travels 14 mph slower than the westbound train and the total distance between them after five hours is 950 miles. The correct calculation leads to a speed of 88 mph for the eastbound train, which is not listed in the available options, implying a possible error in the question or the options provided.
The correct answer is none of all.
Step-by-step explanation:
The question involves determining the rate of an eastbound train given that it travels at a speed that is 14 mph slower than a westbound train, and the two trains are 950 miles apart after five hours. To find the rate of the eastbound train, we can first represent the rate of the westbound train as 'x' mph. Therefore, the eastbound train has a rate of 'x - 14' mph. After five hours, the total distance covered by both trains will be the sum of their individual distances traveled, which equals to 950 miles.
We can then create the equation: 5x + 5(x - 14) = 950 to represent the total distance. Simplifying this gives us: 5x + 5x - 70 = 950, or 10x = 1020, leading us to x = 102 mph. As the eastbound train is traveling 14 mph slower than the westbound train, its speed is 102 mph - 14 mph = 88 mph. However, since this speed is not one of the available options (A) 116 mph (B) 120 mph (C) 122 mph (D) 126 mph, it appears that the provided options do not include the correct answer calculated by the given information.