Let us say, the average speed of the passenger train = x km/h.
Average speed of express train = (x + 11) km/h
Given, the time taken by the express train to cover 132 km is 1 hour less than the passenger train to cover the same distance. Therefore,
($\dfrac{132}{x}$) – ($\dfrac{132}{(x+11)}$) = 1
$\dfrac{132(x+11-x)}{(x(x+11))}$ = 1
$\dfrac{132 × 11 }{(x(x+11))}$ = 1
⇒ 132 × 11 = x(x + 11)
⇒ $x^{2} + 11x – 1452 $= 0
⇒ $x^{2} + 44x -33x -1452$ = 0
⇒ x(x + 44) -33(x + 44) = 0
⇒ (x + 44)(x – 33) = 0
⇒ x = – 44, 33
As we know, speed cannot be negative.
Therefore, the speed of the passenger train will be 33 km/h and thus, the speed of the express train will be 33 + 11 = 44 km/h.