SOLUTION: A train travels 315 miles across the plains in the same time it travels 175 miles in the mountains. If the rate of the train is 40 miles per hour slower in the mountains, find both

Question 265053: A train travels 315 miles across the plains in the same time it travels 175 miles in the mountains. If the rate of the train is 40 miles per hour slower in the mountains, find both the rate in both the plains and mountains.
That is the question, would you be able to help me organize all of this information to solve it?
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
OK
Distance(d) equals Rate(r) times Time(t) or d=rt; r=d/t and t=d/r
Let r=rate of train across the plains
Then r-40=rate of train in mountains
Time travelling across the plains=315/r
Time travelling in the mountains=175/(r-40)
Now we are told that the above two times are equal, so:
315/r=175/(r-40) divide each term by 35 (just to reduce size of the numbers)
9/r=5/(r-40) multiply each term by r(r-40) or cross multiply
9(r-40)=5r get rid of parens
9r-360=5r subtract 9r from each side
9r-9r-360=5r-9r collect like terms
-4r=-360
r=90 mph---------------------rate across the plains
r-40=90-40=50 mph -------------rate in the mountains
CK
315/90=175/50
3.5=3.5

Hope this helps---ptaylor

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