Algebra work problem?

Question

A passenger train cna travel 325 mi in the same time a freight train takes to travel 200 mi. If the speed of the passenger train is 25mi/h faster than the speed of the freight train, find speed of each.

Answer 1

Let's write the problems equations:

passenger train speed = P
freight train speed =F

P*T=325mi
F*T=200mi
P=F+25mi/h

Now we solve the problem:
T=325mi/P and T=200mi/F
Which means 325mi/P=200mi/F
We multiply by P and by F to get
F*325mi=P*200mi or F*325=P*200
But P=F+25mi/h
F*325=(F+25mi/h)*200=F*200mi+5000mi/h
we remove 200mi on both side and we get
F*125=5000mi/h

=>F=5000mi/h /125 = 40mi/h
=>P=40mi/h+25 mi/h =65 mi/h

Answer 2

let p=speed of passenger train
let f=speed of freight train

325/p=200/f
and p=f+25