Question 133198
Distance(d) equals Rate(r) times Time(t) or d=rt; r=d/t and t=d/r

Let r=rate of freight train
Then r+20=rate of passenger train

Time it takes freight train=322/r
Time it takes passenger train=392/(r+20)

Now we are told that the above two times are equal, so:

322/r=392/(r+20)  multiply each side by r(r+20) (or cross multiply)

322(r+20)=392r  get rid of parens

322r+6440=392r  subtract 322r from each side

322r-322r+6440=392r-322r  collect like terms
6440=70r  divide both sides by 70

r=92 mph------------------------------speed of freight train

r+20=92+20=112 mph------------------------speed of passenger train

CK
322/92=392/112
3.5=3.5


Hope this helps---ptaylor