Let's call the speed the train travels for the first scenario as x mph. According to the problem, the train takes 8 hours to travel 320 miles at a speed of x mph.

So, the time taken to travel d distance at the speed x mph is given by the formula: time = distance / speed. Thus, in this case, the time taken is 8 hours, and the distance is 320 miles.

Hence, we can write the equation as: 8 = 320 / x.

Now, let's consider the second scenario. The problem states that the train takes 4 hours less to travel 320 miles at a speed 20 mph faster than the speed it takes to travel the same distance in 8 hours.

So, the speed for the second scenario is (x + 20) mph. The time taken to travel the same distance at this speed is 8 - 4 = 4 hours less than the time taken at the speed x mph.

Using the same formula as before, we have the equation: 4 = 320 / (x + 20).

Now, we can solve these two equations to find the values of x and (x + 20).

From the first equation, we have 8 = 320 / x. Multiplying both sides by x, we obtain 8x = 320. Dividing both sides by 8, we get x = 320 / 8 = 40.

Substituting the value of x into the second equation, we have 4 = 320 / (40 + 20). Simplifying further, we have 4 = 320 / 60 = 16 / 3.

Multiplying both sides by 3 to get rid of the fraction, we get 12 = 16. This is not correct.

Hence, there seems to be an error in the given problem statement. Please check the values and conditions provided again, and I will be glad to assist you further.

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