Question 265053
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