SOLUTION: an express train travel 150 km in the same time that a freight train travel 100 km if the express train goes 2 km per hour faster than the freight train find the rate of each train

Let f be the speed of the freight train in km/h.
Then the speed of the express train is (f+2) km/h.

The condition says that 

 = .

The left  side is the time for the express train to cover 150 km.
The right side is the time for the fraight train to cover 100 km.

To solve the equation, multiply both sides by f*(f+2). You will get

150f = 100(f+2),

150f = 100f + 200,

150f - 100f = 200,

50f = 200,

f =  = 4 km/h.

The speed of the freight train is 4 km/h.
The speed of the express train is 4+2 = 6 km/h.