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Two trains leave the station at the same time, one heading west and the other east. The westbound train travels 14 mph faster
than the eastbound train. If the two trains are 340 miles apart after two hours, what is the rate of the westbound train?
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Let x be the rate of the eastbound train in miles per hour (mph).
Then the rate of the westbound train is (x+14) mph.
The eastbound train covered 2x miles in two hours.
The westbound train covered 2(x+14) miles in two hours.
So, the equation is
2x + 2*(x+14) = 340.
Simplify and solve for x:
2x + 2x + 28 = 340,
4x = 340 - 28,
4x = 312,
x = = 78 mph.
Answer. The rate of the eastbound train is 78 mph.
The rate of the westbound train is 78 + 14 = 92 mph.