SOLUTION: The speed of a passenger train is 18 mph faster than the speed of a freight train. The passenger train travels 320 miles in the same time it takes the freight train to travel 230 m

Question 307199: The speed of a passenger train is 18 mph faster than the speed of a freight train. The passenger train travels 320 miles in the same time it takes the freight train to travel 230 miles. What is the speed of each train?
Passenger?
Freight?
Found 2 solutions by mananth, texttutoring:
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
The speed of a passenger train is 18 mph faster than the speed of a freight train. The passenger train travels 320 miles in the same time it takes the freight train to travel 230 miles. What is the speed of each train?

let speed of freight train be x mph
freight train travels 230 miles
time taken = 230/x
.
passenger train speed will be x+18 mph
time taken = 320/x+15
these two times are equal
230/x = 320 / x+18
230(x+18)=320*x
230x +4140 =320x
-90x=-4140
x= 46 mph the speed of the freight train
46+18 = 64 mph is the speed of the passenger train
Ananth

Answer by texttutoring(324) (Show Source): You can put this solution on YOUR website!
Let's write down everything we know. I will use p to denote Passenger train, and f to denote Freight train. Note that v is velocity (which is another word for speed).
Dp=320 miles
Df=230 miles
Vp=Vf+18
Vf=?
Tp=Tf

The fact that the times are equal is very important. We will use the distance speed formula, D=VT, to solve. Let's rearrange the formula so that it is isolated for T. D/V = T

So Dp/Vp = Tp and Df/Vf = Tf

Now we can set the two equations equal to each other, because Tp=Tf:

Dp/Vp = Df/Vf

320/(Vf+18) = 230 / Vf

Cross multiply to get rid of the denominators:

320Vf = 230Vf + 4140
90Vf = 4140
Vf = 4140/90
Vf=46

Vf=46mph

The passenger train is 18 mph faster than the freight train, so Vp =46+18 =64mph

Freight Train speed = 46 mph
Passenger train speed = 64 mph
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