Question 91981

Let r=speed(rate) of freight train

Then r+25=speed of passenger train

distance(d)=rate(r) times time(t) or d=rt; r=d/t and t=d/r

time it takes freight train=200/r

time it takes passenger train=325/(r+25)

Now we are told that the above two times are the same.  Soooooooooo

200/r=325/(r+25) multiply both sides by r(r+25) to get rid of fractions

200(r+25)=325r  get rid of parens

200r+5000=325r  subtract 5000 and also 325r from both sides

200r-325r+5000-5000=325r-325r-5000  collect like terms

-125r=-5000  divide both sides by -125

r=40 mi/hr------------------------speed of freight train

r+25=40+25=65 mi/hr---------------------speed of passenger train

CK

200/40=325/65
5=5


Hope this helps----ptaylor