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 11km/h more than that of the passenger train, find the average speed of the two trains.

Let, the speed of passenger train = x Km/h
Therefore, the speed of express train = x + 11 km/h
Distance travelled = 132 Km
Time taken by passenger tarin t₁ = 133/x hours [As, time = distance/speed]
Time taken by express train t₂ = 132/x+11 hours
According to question,
132/x = 132/x + 11 = 1
⇒ 132/x = 132/x + 11 = 1
⇒ 132(x + 11) – 132x/x(x + 11) = 1
⇒ 132x + 1452 – 132x = x(x + 11)
⇒ 1452 = x² + 11x
⇒ 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
Either x = -44 or x = 33
But x ≠ -44, as x is the speed of train, which can’t be negative. So, x = 33
Hence, the speed of passenger train = 33Km/h
The speed of express train = 33 + 11 = 44Km/h