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.

Asked by khushdab | 31st Mar, 2020, 02:00: PM

Expert Answer:

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.

Answered by Renu Varma | 31st Mar, 2020, 06:03: PM