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

Solution:

Let the average speed of the passenger train be x km/h

The average speed of the express train will be (x + 11) km /h

As we know that, Distance = Speed × Time

Time = Distance / speed

Therefore, time taken by the passenger train to travel 132 km = 132 / x

Time taken by the express train to travel 132 km = 132 / (x + 11)

The difference between the time taken by the passenger and the express train is 1 hour. Therefore, we can write:

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

Solving 132 / x - 132 / (x + 11) = 1 by taking the LCM on the LHS:

[132(x + 11) - 132x] / x (x + 11) = 1

[132x + 1452 - 132x] / (x² + 11x) = 1

1452 = x² + 11x

x² + 11x -1452 = 0

By comparing x² + 11x - 1452 = 0 with the general form of a quadratic equation ax² + bx + c = 0, we get a = 1, b = 11, c = - 1452 

b² - 4ac = 11² - 4(1)(-1452)

= 121 + 5808

= 5929 > 0

b² - 4ac > 0

Therefore, real roots exist.

x = [- b ± √ (b² - 4ac)] / 2a

= (-11 ± √ 5929) / 2

= (-11 ± 77) / 2

x = (- 11 + 77) / 2 and x = (- 11 - 77) / 2

x = 66 / 2 and x = - 88 / 2

x = 33 and x = - 44

x can’t be a negative value as it represents the speed of the train.

Thus, speed of the passenger train = 33 km/hr

Speed of the express train = x + 11 = 33 + 11 = 44 km/hr

☛ Check: NCERT Solutions Class 10 Maths Chapter 4

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Video Solution:

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

Class 10 Maths NCERT Solutions Chapter 4 Exercise 4.3 Question 10

Summary:

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 an express train is 11km /h more than that of a passenger train, then the average speed of the passenger train is 33 km/h and the speed of the express train is 44 km/h.

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