# Math

The The speed of a passenger train is 12 mph faster then the speed of a freight train. The passenger train travels 270 miles in the same time it takes the freight train to travel 210 miles. Find the speed of each train.

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1. If we take the speed of the freight train to be x, and the speed of the passenger train to be y, we get that:

1)y=x+12
2)270/y=210/x

So if we replace y in the second equation by the y we found in the forst equation, we get that:

270/(x+12)=210/x
=>210*(x+12)=270x
=>60x=2520
=>x=42
=>y=54

So the freight train moves at 42mph and the passenger train moves at 54mph

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2. Let the speed of the freight train be x mph
then the speed of the passenger train is x+12 mph
Time for freight train = 210/x
time for passenger train = 270/(x+12)

but they are equal so....

270/(x+12) = 210/x

cross-multiply and solve.
Let me know what you got.

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3. The speed of a passenger train is 18 mph faster than the speed of a freight train. The passenger train travels 310 miles in the same time it takes the freight train to travel 220 miles. Find the speed of each train.

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