Question

The speed of passenger train is less than that of an express train by 20 km per
hour. Find the average speed of both the trains.

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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.

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Answer

Let x km per hour be the average speed of the passenger train, then the average speed of the express train will be (x+11) km per hour.

The time taken by the passenger train is

x

132

hour and the time taken by the express train is

(x+11)

132

hour. So,

x+11

132

=

x

132

+1

x

2

+11x−1452=0

x

2

+44x−33x−1452=0

(x−33)(x+44)=0

x=33,x=−44

The speed cannot be negative, so the speed of the passenger train is 33 km per hour and the speed of the express train is 33+11=44 km per hour.