Quadratic Equations.

Vex = speed of the express train, and Vps = speed of passenger train,

300/Vex + 2 = 300/Vps

and

Vex - Vps = 30

which gives Vex = 30 + Vps

Using this relation in the first equation,

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

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

300Vps + 60Vps + 2Vps² = 9000 + 300Vps

2Vps² + 60Vps - 9000 = 0

Vps = {-60±(3600-4x2x-9000)}/4,

We find Vps = 53.74 km/hr.

and Vex = 83.74 km/hr.

Regards,

Team,

TopperLearning.