A passenger train leaves a station at 6. am followed by an express train which leaves at 6:30 am and travels 20 km faster than the passenger train. The express train arrives at a station 90 km away, fifteen minutes before the passenger train. Calculate their speeds.

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

Therefore, speed of the express train will be (x+20) km/hr.

Let the time taken by the passenger train to travel 90 km be T and that by express train be t.

As per the question, time of departure t=T-0.5 and Distance D = 90 km

According to the time of arrival, t=T-15/60

Therefore, total time taken by express train t = T - 30/60 - 15/60

90/(x+20)=90/x - (30+15)/60

Solving this, we get

x²+20x-2400=0

Solving the quadratic equation, we get

x = -60 or x = 40

Since, x can't be negative

Therefore, x is 40.

Hence, the speed of passenger train is 40 km/hr and that of express train is 60 km/hr.