Question 482188
*******The speed of a passenger train is 14 mph faster than the speed of a freight train,****** 
Therefore,
Spd of freight train=x
Spd of passanger train =x+14


*****The passenger train travels 250 miles in the 'same time' it takes the freight train to travel 180 miles.***** 
So we know that 
Distance travelled by passenger train =250miles
Distance travelled by freight train= 180 miles
Let T be the Time which is the same for both trains to travel their respective  distances.


------------------------
{{{speed=dist/time}}}
------------------------


Freight train:
{{{x=180/t}}}
{{{t=180/x}}}


------------------------
Passanger Train:
{{{x+14=250/t}}}
{{{t=250/(x+14)}}}


-------------------------
So,
{{{180/x=250/(x+14)}}}
**********(we leave the time(t) out as it is the same)*********
{{{180(x+14)}}}=250x
{{{180x+2520=250x}}}
{{{-70x=-2520}}}
{{{x=36mph}}}

So speed of Freight Train=36mph.
Spd of passanger Train={{{x+14}}}={{{36+14}}}=50mph.



******Same Problem Without all the explanation*********


Passenger train:
distance = 250 miles ; rate = x+14 mph ; time = 250/(x+14) hrs.
---------------------
Freight train:
distance = 180 miles ; rate = x mph ; time = 180/x hrs
-----
Equation:
time = time
{{{250/(x+14) = 180/x}}}
---
{{{180(x+14)=250x}}}
{{{180x+2520=250x}}}
{{{-70x=-2520}}}
{{{x=36mph}}}

x = 36 (rate of the freight train)
x+14 = 50 (rate of the passenger train)