Question

An express train takes 1 hour less than a passenger train to travel 132 km between Mysore and Bangalore (without taking into consideration the time they stop at intermediate stations). If the average speed of the express train is 11 km/hr more than that of the passenger train, find the average speed of the two trains.

Answer 1

Let the speed of the passenger train = x kmph. 

Then speed of the express train = x + 11 kmph. 

Distance travelled = 132 km 

We know that time = \(\frac{distance}{speed}\)

⇒ x² + 11x = 13 × 11 

⇒ x² + 11x – 1452 = 0 

⇒ x² + 44x – 33x – 1452 = 0 

⇒ x(x + 44) – 33 (x + 44) = 0 

⇒ (x + 44) (x – 33) = 0 

⇒ x + 44 = 0 (or) x – 33 = 0 

⇒ x = -44 (or) x = 33 

But x can’t be negative. 

∴ Speed of the passenger train = x = 33 kmph. 

Speed of the express train = x + 11 = 44 kmph.