Question

Two trains leave Santa Fe at the same time, one going east and the other west. The train going west travels 30 mph faster than the train going east. If the trains are 260 miles apart after 2 hours, how fast is each train traveling?

a) The eastbound train is traveling at 65 mph, and the westbound train is traveling at 95 mph.
b) The eastbound train is traveling at 95 mph, and the westbound train is traveling at 65 mph.
c) The eastbound train is traveling at 125 mph, and the westbound train is traveling at 155 mph.
d) The eastbound train is traveling at 155 mph, and the westbound train is traveling at 125 mph.

Answer 1

After setting up equations based on the given rates and distances, it is determined that the eastbound train travels at 50 mph and the westbound train at 80 mph. However, these speeds do not match any options provided in the question, indicating a possible error.

Step-by-step explanation:

To solve the problem of finding the speed of each train, we can set up two equations based on the information given. Let's denote the speed of the eastbound train as x mph and therefore the westbound train as x + 30 mph. After 2 hours, the distance covered by the eastbound train is 2x miles, and the distance covered by the westbound train is 2(x + 30) miles. The total distance between the two trains after 2 hours is given as 260 miles.

Adding these two distances gives us an equation: 2x + 2(x + 30) = 260. Simplifying, we get 4x + 60 = 260, or 4x = 200. Dividing both sides by 4 yields x = 50. Therefore, the eastbound train is traveling at 50 mph, and the westbound train is at 50 + 30, which equals 80 mph.

None of the given options (a, b, c, d) match these calculated speeds, so it seems there might be an error in the question or the options provided.