(Q28) 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/hr more than that of the passenger train, find the average speed of the two trains.

Answer:

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 =
distance
speed
By problem
132
x
 -
132
x + 11
 = 1

= 132(
1
x
 -
1
x + 11
 ) = 1

=
x + 11 - x
x(x + 11)
 =
1
132

=
11
x2 + 11x
 =
1
132

x2 + 11x = 13 × 11

x2 + 11x - 1452 = 0

x2 + 44x - x - 1452 = 0

x(x + 44) - (x + 44) = 0

(x + 44) (x - ) = 0

x + 44 = 0 or x- = 0

x = -44 or x =

But x can't be negative.

∴ Speed of the passenger train = x = kmph.

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