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1. The question asks us to find the speeds of the two cars - z and y.

2. On one day, the two cars are parked at mile zero on a straight road, and they begin moving at the same time in the same direction. After 2 hours 30 minutes, the distance between the cars is 25 miles. Time multiplied by velocity is distance and we know the difference between the traveled distances of the 2 cars. So, we can put together an equation: \(2.5 * z - 2.5 * y = 25 = 2.5(z - y) \rightarrow z - y = 10\).

3. On another day, the cars are parked 25 miles apart on the same road, and they begin moving at the same time toward each other. In 30 minutes, the cars pass each other. Here we can change the problem into a car with a speed z + y traveling 25 miles in 30 minutes. Now, let's put together an equation: \(z + y = \frac{25}{0.5} = 50\).

4. There are two equations: \(z - y = 10\) and \(z + y = 50\). Summing them together gives us \(2z = 60 \rightarrow z = 30\) and then \(y = 50 - 30 = 20\).

5. Our answer will be: y = 20 and z = 30.
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