# 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/hr more than that of a passenger train, find the average speed of the two trains

**Solution:**

Let the average speed of passenger train = x km/hr

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

As we know that, Distance = Speed × Time

Time= Distance / speed

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

Time taken by 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] / x^{2} + 11x = 1

1452 = x^{2} + 11x

x^{2} + 11x -1452 = 0

By comparing x^{2} + 11x - 1452 = 0 with the general form of a quadratic equation ax^{2} + bx + c = 0, we get a = 1, b = 11, c = - 1452

b^{2} - 4ac = 11^{2} - 4(1)(-1452)

= 121 + 5808

= 5929 > 0

b^{2} - 4ac > 0

Therefore, real roots exist.

x = (-b ± √ (b^{2} - 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.

Speed of passenger train = 33 km/hr

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

**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 /hr more than that of a passenger train, find the average speed of the two trains

### Class 10 Maths NCERT Solutions - Chapter 4 Exercise 4.3 Question 10:

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 /hr more than that of a passenger train, find the average speed of the two trains

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 /hr more than that of a passenger train, then the average speed of two trains are such that the passenger train is 33 km/hr and the speed of the express train is 44 km/hr