SOLUTION: a passenger train can travel 325 mi in the same time a freight train takes to travel 200 mi. if the speed of the passenger train is 25 mi/h faster than the speed of the freiht trai

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Question 120468: a passenger train can travel 325 mi in the same time a freight train takes to travel 200 mi. if the speed of the passenger train is 25 mi/h faster than the speed of the freiht train, find the speed of each.
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Distance(d) equals Rate(r) times Time(t) or d=rt; r=d/t and t=d/r

Let r=rate (speed) of the freight train
Then r+25=rate of the passenger train
Time for freight train to travel 200 mi=200/r
Time for passenger train to travel 325 mi=325/(r+25)
Now we are told that the above two times are equal, so:
200/r=325/(r+25) multiply each side by r(r+25){or cross-multiply}
200(r+25)=325r get rid of parens
200r+5000=325r subtract 200r from both sides
200r-200r+5000=325r-200r collect like terms
125r=5000 divide both sides by 125
r=40 mph-----------------------------------speed of freight train
r+25=40+25=65 mph-----------------------------speed of passenger train
CK
200/40=325/65
5=5
Hope this helps---ptaylor