SOLUTION: The speed of a passenger train is 14 mph faster than the speed of a feight train. The passenger train travels 400 mi in the same time that it takes the freight train to travel 330

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Question 132806: The speed of a passenger train is 14 mph faster than the speed of a feight train. The passenger train travels 400 mi in the same time that it takes the freight train to travel 330 mi. Find the speed of each train.
Answer by solver91311(24713) About Me  (Show Source):
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Remember that distance equals rate times time, or d=rt.

If the rate of the freight train is r, then the rate of the passenger train is r + 14.

We can rewrite d=rt as t=d%2Fr.

For the freight train: t=330%2Fr, and for the passenger train: t=400%2F%28r%2B14%29. We know that the times are equal because the problem says "same time", so we can say:

400%2F%28r-14%29=330%2Fr

To solve a proportion, first cross-multiply:
400r=330%28r%2B14%29

400r=330r%2B4620

400r-330r=4620

70r=4620

r=66

The speed of the freight train is 66 mph, and the speed of the passenger train is 66 + 14 = 80 mph.

Check:
400%2F80=5hours

330%2F66=5hours

The times are the same, so the answer checks.