Quadratic Equations.

Let the speed of the passenger train be x km/hr.

Total distance covered = 300 kms

Speed of the express train = (x + 30)km/hr

Time taken by the passenger train = (t + 2)hr

Time taken by the express train = t hr.

Now using the formula for speed.

x = 300/ (t+2) .......(2)

x + 30 = 300/t

t = 300/(x+30) ........(1)

Equating (1) in (2), we get

x = 300/ (300/(x+30) +2)

  = 300/( (300+2x+60/ (x+30))

 = 300 (x + 30)/ (360 + 2x)

360 x + 2x² = 300x + 9000

2x² + 60x - 9000 = 0

x² + 30x - 4500 = 0

Solving this quadratic equation, we get x = 53.73 km/hr.

So, the speed of passenger train is 53.73 and the express train is 83.73.